They did settle some parts of South Germany, but their presence was of course much stronger in East and North Germany.
As for Slavs in South Germany
(in Bavaria / Bayern) - there is a good German publication about them (written in German):
Hans Losert, "Moinvinidi, Radanzvinidi und Nabavinida. Geschichte und Archäologie der Slawen in Bayern", 2009.
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Those particular Slavic tribes which settled in Bavaria aren't well-known today because they were Christianized very early on (compared to other Slavic tribes) and were among first West Slavic groups which got Germanized. Slavs in Franconia (today north-eastern Bavaria) became part of the Frankish state at some point after 740 and became Christianized by Charlemagne around year 800, when he ordered to construct 14 churches for them. Those Slavic tribes were called Moinwinidi and Radanzwinidi (and also Nabavinida) and they lived along the rivers Main and Regnitz,
as Charlemagne's document from year 794 AD reveals:
"(...) in terra Sclavorum, qui sedent inter Moinum et Radentiam fluvios, qui vocantur Moinwinidi et Radanzwinidi."
In English:
"(...) in the land of Slavs, who live between rivers Main and Regnitz, who are called Moinwinidi and Radanzwinidi."
Assimilation of those Slavs in Bavaria lasted several centuries. In year 1162 we still have Slavic names among them (for example certain guys Dragan and Gleische from Effelder near Coburg); in 1233 in Herzogtum Meranien we have a certain important guy Konrad Slavir. Slapansgereute (Schlappenreuth) near Bamberg is a settlement founded by Slapan, who was Slavic. His descendants can be traced in sources until the 15th century. According to historian Erwin Herrmann the family of Walpoten from Franconia was also Slavic - their castles have names of Slavic origin (Trebgast, Zwernitz). Medieval von Slawendorf family were also Franconian Slavs. Slavic population of Slawendorf (later called Altenstadt, today part of Bayeruth) preserved their language until the 14th century, as there are 14th century documents which say about Slavic inhabitants there. Near Weichenwasserlos there is a toponym Grotze suggesting existence of a Slavic castle. This Grotze is surrounded by settlements with names of Slavic origin - Granitz auf der Dobrich, Dobdansdorf in den Tibitzen, in der Peusteritz. Graitzstein, Greyczberg near Staffelstein, Marktgraitz, Teunz are other former Slavic castles in the region. German summary of the article about those Slavic tribes by Jerzy Strzelczyk:
http://s9.postimg.org/qxyj9j8pr/Slavs_in_Franconia.png
The following was the approximate maximum extent of Slavic early westward expansion and compact (large-scale) settlement - which was around year 850 AD: Starting from the north-west, compact Slavic settlement (not including some individual, dispersed Slavic communities which had migrated even farther west but lived in ethnically mixed areas in which Slavs were never majority) encompassed the following westernmost regions: Fehrman island, Wagrien (Wagria), outskirts of Hamburg, Lauenburg region, Lüneburger Heide, Wolfsburg region, Magdeburg region. South of Magdeburg the boundary of ethnic Slavic territory can be drawn as a meridional line extending up to Erfurt and the eastern part of the Thüringer Wald. From the Thüringer Wald the boundary was a line extending in south-western direction up to the River Main and the outskirts of Bamberg. From Bamberg the 9th century Slavic-Germanic ethnic boundary sharply turned towards Austrian Linz, and then once again turned meridionally, extending up to the Alpine city of Liezen at the River Enns. In the Alps groups of Slavs migrated through mountain valleys up to eastern Tirol and the Upper Drava River. There was also large-scale Slavic settlement in the Julian Alps, in area north-west of Udine, and in what is today the Provincia di Gorizia of Italy. Slavic westward colonization did cross the Saale River, in the following area: from the southern outskirts of Magdeburg, through the area of Erfurt, and up to the Thüringer Wald and the Main River near Bamberg - situation in year ca. 850 AD was roughly like this:
http://s27.postimg.org/diabe9q2r/Slavs_west_of_the_Saale.png
One group of Slavs migrated even as far as the Rhine - but in that area they were just a Slavic drop in a sea of other ethnicities.
There was also a time - from year 804 to year 809 - when Slavs, united with Charlemagne, fought against Saxons. At that time Slavs captured the region of future Hamburg (at that time it did not yet exist, as it was built by Charlemagne in 808-809) and all lands of Northern Saxons - known as Nordalbingia. I'm not sure if significant numbers of Slavs actually settled there, but some did (read below). During those 5 years Slavs had access to the North Sea. In 880 Slavs captured Hamburg in cooperation with the Danes. And in 983 Slavs (the Obotrites under king Mstivoj) once again captured and destroyed Hamburg, this time on their own.
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Timeline of the early phase of history of Slavs in Germany, from the beginning of historical record until the death of Charlemagne:
⦁ 512 - the Heruli migrate from middle Danube to North Germany and encounter territories already inhabited by Slavs on their way there (Procopius)
⦁ 6th century - Slavic settlement at Prague numbers over 600 houses:
http://www.archaeobotany.org/download/posters/novak_roztoky_abstract_whv2010.pdf
⦁ ca. 550 - Slavs start migrating into what is now East Germany
⦁ 595 - Slavs (probably ancestors of Slovenes or / and Croats) fight against Frankish-dependent Bavarian duke Tassilo in modern Austria and Bohemia
⦁ 596 - Slavs, probably allied with the Avars, defeat the Bavarians under Tassilo, killing 2,000 of them
⦁ 610 - battle of Aguntum (4 km to the east of present-day Lienz), Bavarians finally stop Slavic westward expansion in this region (Paul the Deacon)
⦁ 620s - a major war between Slavs and Avars (who had previously been allies)
⦁ 624 - a smuggler of weapons from the Frankish Empire, Samo (born near Sens at the Yonne river in central France), who had previously been illegally smuggling across the border and selling weapons to Slavs, enters Slavic lands, joins Slavs in their fight against the Avars, and due to his merits in battle, united Slavic tribes elect him their king (source: Fredegar's chronicle). Samo was probably a Gallo-Roman.
⦁ 630 - Walluk, duke of Carantanians (northern Slovenes), joins Samo's Federation.
⦁ 631 - Slavic Federation defeats the Frankish Empire in the battle of Wogastisburg
⦁ 631 - after the victory at Wogastisburg Slavic armies invade and plunder Thuringia
⦁ 632 - Dervan, duke of Surbi (Sorbs) joins the Slavic Federation under king Samo
⦁ 636 - Dervan is killed in one of battles against Randulf, governor of Thuringia
⦁ 661 - the federation disintegrates into many realms again after Samo's death. According to Fredegar's chronicle Samo had 12 Slavic wifes, 22 sons and 15 daughters.
⦁ 772 - Charlemagne invades Southern Saxons
⦁ 777 - conquest of Southern Saxons is completed
⦁ 780 - first Frankish contact with the Obodrites at the Middle Elbe
⦁ 782 - Sorbs raid and plunder Thuringia and Frankish-controlled Saxony
⦁ 782 - Saxon uprising against Franks under Widukind. Obodrites side with Franks
⦁ 785 - uprising squashed, Widukind surrenders and adopts Christianity in Attigny
⦁ 789 - Wieczan (Witzan) becomes the supreme duke (rex / princeps) of Obodrites
⦁ 789 - Obodrites mentioned as "old good allies" of Charlemagne (against Saxons)
⦁ 789 - Wieczan asks Charlemagne for assistance against his troublesome eastern neighbours, the Holy Union of the Veleti, under supreme duke Drogowit.
⦁ 789 - Charlemagne, allied with Frisians, Sorbs and Obodrites (under duke Wieczan), invades Veleti. Frankish army crosses the Elbe near modern Wolmirstadt. Allied forces besiege Brenna, the main stronghold of Veleti duke Drogowit. Seeing that resistance is pointless, Drogowit negotiates peace. Veleti pay a single tribute to Charlemagne. Charlemagne satisfied with tribute returns back to Francia.
⦁ 795 - Obodrite duke Wieczan (dux Witzan), ally of Franks against Nordalbingians (northernmost Saxon tribe, who remain independent from Frankish rule).
⦁ 795 - at the Elbe near Bardowick Nordalbingians ambush Obodrites, killing Wieczan
⦁ ca. 796 - Drozko elected new rex / princeps of the Obodrites. Drozko has a son named Czedrog (Chedrog). Drozko continues pro-Frankish policies of Wieczan and Charlemagne is his ally. Danes, Northern Saxons and Veleti are his enemies.
⦁ 795-798 - in revenge for Wieczan's death, Charlemagne raids Nordalbingians and carries out first forcible population transfers and deportations of Saxons.
⦁ 798 - battle of Swentana (Bornhöved) between Obodrites under Drozko and Nordalbingians (at the same time Charlemagne's army is near Minden, raiding Ostphalia). Obodrites win. About 3 - 4 thousand Saxons perish.
⦁ 799 - son of Charlemagne mediates in conflict between Obodrites and Veleti
⦁ 804 - conquest of Nordalbingians by Franks (with Veleti help) is completed, forcible deportation of over 10,000 Nordalbingian men, with families, to Gaul.
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804 - in Hollenstedt at the Elbe Drozko is crowned King by Charlemagne, he is also awarded Nordalbingia, which becomes part of the Slavic Obodrite realm (sources: Ann. Regni Francorum a 804, Chron. Moiss a 804). Archaeological evidence of Slavic settlements and pottery in Nordalbingia discovered in Hamburg and in Domplatz, dated to 8th-9th centuries (R. Schindler connects these with Drozko's reign).
⦁ ca. 805 - Charlemagne fortifies Frankish-Slavic border (limes sorabicus and limes saxonicus) and establishes permanent military posts along it. He introduces capitulare duplex in 805 - a kind of embargo for export of weaponry to Slavic lands (including even his allied Obodrites). Several places are chosen for trade with Slavs.
⦁ 805 - Franks invade the Sorbian-Lusatian tribe of the Glomaci
⦁ 805 - duke Lecho of the Bohemians (Czechs) dies in battle against Charlemagne
⦁ 806 - Sorbs (Siurbs) agree to pay tribute to Charlemgne after their duke - Miliduch (Milidouch / Milito) - is killed in a battle against Franks near modern Halle.
⦁ 808 - Drozko, king of the Obodrites. Godelaib, one of their minor dukes.
⦁ 808 - the Danes under duke Godfred (his realm is in Jutland), allied with the Veleti, invade the Obodrite realm (Jutland had previously become a refuge for Saxon refugees during Frankish-Obodrite invasions of Nordalbingia). Danes and Veleti manage to capture several Obodrite strongholds in the process.
⦁ 808 - at least two out of member-tribes of the Obodrite realm, Smolincy and Linianie, betray and unite with Danish-Veleti army. King Drozko is forced to abandon his realm and escapes to Francia. Godelaib is captured and executed. Godfred annexes Nordalbingia, two other Obodrite provinces - Obodrsko and Wagria - pay tribute.
⦁ 808-809 - Veleti wage offensive war against Obodrites and then against Franks
⦁ 808 - Charlemagne sends his son to crush the Veleti and Obodrite traitors, but he is defeated and has to retreat. Godfred proposes peace to Charlemagne, negotiations take place in Bandenflut at the Stör River, but they fail and war continues on.
⦁ 809 - Drozko returns from exile to his country. He signs truce with Danes in exchange for giving them one of his sons (maybe Chedrog) as a hostage. He allies with Saxons against Veleti and these Obotrite trines which seceded from his realm. Allied Obodrite loyalists and Saxons besiege a stronghold of Smolincy at Connoburg. The stronghold is captured and destroyed, power over rebellious tribes is restored.
⦁ 809 - Godfred violates the truce and invades Obodrites, he demolishes Slavic coastal town at Rerik (near modern Wismar), and deports local merchants to Haithabu (Hedeby), Denmark. Drozko is killed by Danish assassins at Rerik.
⦁ 809 - after the death of Drozko Charlemagne deprives the Obodrites of Nordalbingia and incorporates it to his Empire. The land is depopulated due to war, disease and deportations, so he brings in new settlers from entire Empire. Charlemagne establishes three new castles to strengthen the defence of his borders: first is at Eselfeld at the Stör River, second is at Hamburg, third is at Hochbucki near Lenzen at the Elbe.
⦁ 810 - Veleti attack the Frankish Empire and destroy their new castle at Hochbucki
⦁ 812 - Franks and Obodrites (under their new grand duke, Slavomir) in retaliation invade Veleti territories and manage to force them to pay a tribute.
⦁ 813 - coronation of Louis I by Charlemagne in Aachen.
⦁ 814 - death of Charlemagne, Louis I takes power in the Empire. Those of Slavic tribes which had been paying tribute to Charlemagne, stop paying it.