Hmmm. 7 days are different than 10 days. And a slower pace means different things to different people.
I am assuming that this is your first trip to Italy, so you've got a blank canvas. So here's the thing--are you saying you want to stay in one place for the duration, a small 'relaxing' hamlet? Does that mean away from crowds? That might be a little hard to do in September, unless you find an obscure village that nobody knows about. In theory, it's great to say, ah, we'll meet locals, immerse ourselves in the culture of the village. In practice, it can be a little different. Tourists have trampled almost every inch of the country.
I am partial to southern Italy & Sicily, not the most popular choices on this board, but to each to his own, right? If I had only 7 days, (6 nights?), I'd find a picturesque base--like Ravello on the Amalfi Coast, which would give you a lot of easy options if you wanted to daytrip. If you didn't, no problem, enjoy Ravello and the wonderful surrounding towns like Positano & Maiori with the seafood-based cuisine and the great Campania wine. On our trip, we based in Salerno--just off the peninsula--and daytripped it to Pompei & Amalfi, besides being in a pretty, coastal Italian small city also with great food & transportation.
If you had 10 days (9 nights?) I would start off the trip by flying into Catania, Sicily and taking private transport about 30 km north for approximately three days in Taormina. It is just as picturesque as the Amalfi Coast, but in a different way. Plenty of Greek, Norman, German & Arab influences. Exotic. Warm people. Mt. Etna looms nearby. You would love it. Then you could fly Catania to Naples (more efficient) and on to Ravello for the rest of your trip, or take a walk on the wild side and try the train/ferry across the Strait of Messina and up to Naples.
Whatever you pick, you cannot go wrong, Enjoy your planning!