The budget options for staying in Italy are quite extensive. All large cities have numerous options including hostels, camping grounds and monasteries/convents which often operate for female travellers only. Camping grounds tend to be a little further out of town so may hinder night time entertainment plans but do offer substantial savings. Often they also have bungalows, cabins or dorm style beds so you may not need a tent. If you plan to stay long term somewhere you maybe able to work out an arrangement with the manager but some places do not enourage long term guests and may impose a maximum stay.
Yaif offers cheap long term accommodation in apartments around Italy. However in some countries hotel rooms for two or pension type establishments can work out cheaper.
For more detalies visit the website: http://www.yaif.it