Any place can be cheap depending on how you travel. For people who are on a tight budget staying in youth hostels or camp sites, and cooking by yourself (youth hostels usually have free kitchens for guests) is the best way to go.
It's not possible to give general recommendations about a 'cheap destination' as the most expensive part of a budget trip is often the transportation (flight, train, bus) to the destination. It is fallacious logic to seek to go to poorer countries to save money as, for Westerners at least, this means travelling more far and ending up paying a lot for the flight to reach the destination.
Giorgi recommends Georgia (selflessly of course, being Georgian), but there are no cheap flight from most European countries to Georgia, so that can never be considered a budget trip.
It's not possible to give general recommendations about a 'cheap destination' as the most expensive part of a budget trip is often the transportation (flight, train, bus) to the destination. It is fallacious logic to seek to go to poorer countries to save money as, for Westerners at least, this means travelling more far and ending up paying a lot for the flight to reach the destination.
Giorgi recommends Georgia (selflessly of course, being Georgian), but there are no cheap flight from most European countries to Georgia, so that can never be considered a budget trip.