Ciao tutti! I'm not Italian but I'm living here, and I can tell you that you can definitely eat well without a lot of carbs - avoid pasta and pizza of course. There's lots and lots of cheeses, for example. All the bigger stores have "bio" sections where you can find lots of high quality legumes, veggies etc., and there is indeed greek yoghurt - however a word of caution wrt yoghurts... it's really difficult to find yoghurts without flavourings here. So look out for the "carboidrati" levels
I can recommend shopping at Pam, Coop and Lidl. Pam is the most expensive one but usually has good quality stuff and a large selection.
If you eat meat then going to restaurants isn't a problem at all. If you're a veggie like me then don't expect it to be any easier than usual
In general you can find any restaurant you want with whichever cuisine you desire - Italians love all food.