Yes, old town can be touristy and "buzzy" but still no better taste of France and Italy in one place. We have stayed dozens of times in or near Rosetti and are always rewarded with great people watching and human entertainment. Chez Juliette is very close (slightly uphill and on the right) it is a wonderful small dinner restaurant with a splendid duck confit. In the plaza itself there is a good brasserie for lunch called "La Claire Fontaine" have the mussels, you will be happy you did.
If you are looking for a perfect place to spend a few nights try renting a flat from "Nice Pebbles" they are reliable and leave no details unattended. Owned by an English couple they have all sorts of rentals in every price range----we are NEVER disappointed (www.nicepebbles.com).
We have been to Nice many times and sometimes hear that old town is too crowded or touristy. It is one of the few places that I would say "who cares!" it is a splendid place to call home while you explore the area. Have fun!