Consider Friuli, Peaches. We went at Easter last year and found it very cheap. I wouldn't recommend the accommodation we had (very dodgy DIY-build job...!) but it was cheap, and also cheap to eat out ('standard' fare, like pasta, pizzas and so on... I'm not talking swanky restaurants). From Friuli we went to Venice for the day twice. You can also get into the mountains (or at least the beginnings of them) from there (the Alpi Giulie/Julian Alps) and down to the coast (Grado is a nice seaside-y place). Trieste is an interesting city (go to Miramare) and I heartily recommend a visit to the mosaics in the basilica at Aquileia (sounds a bit limited in appeal, I know, but honestly, they are amazing!). We stayed in the area near Spilimbergo/San Daniele (famous for its ham).
Wherever you go in Italy you will be able to find food that doesn't break the bank. (Even in Florence and Venice, honestly.) Just avoid the obvious tourist traps and ask locals where they would go to eat.
If you stick to the idea of going to the south, I think you'll find it is a lot cheaper. (Sorry, I don't know the south as well.) But my advice would still be to talk to locals (e.g. if you are self-catering, the owners of the property you're renting) and ask them where they would recommend that is not too expensive.
Have you considered looking at agriturismi? These are places in the country which have accommodation (either on a B&B basis or basic self-catering) but which often also provide home-cooked food if you want it in the evenings (and possibly even packed lunches too). Again, my experience is in the North, but you'll find similar stuff in the south too.
Hold on... I've got an agriturismo site saved somewhere... I'll go and get you a link...