I would recommend the Amalfi Coast area. I would suggest being based out of Sorrento (as it is perfect for what you described as ideal), and tour up and down the coast on different days. It is an amazingly beautiful area, with some of the best food in all of Italy.
From there you can also visit:
island of Ischia- more luxurious
island of Capri- more touristy, but still beautiful
There shouldnt be the typical bumper to bumper summer traffic that typically plagues the Amalfi Coast, however you may find many more tour buses trying to navigate the narrow two lane road. I would try to hire a cab driver for the day or multiple days. See if the hotel has any drivers they would recommend. They will take you to the best spots, leave you to sight-see and pick you up at a pre-determined location/time.
The water might still be too cold for swimming depending on your tolerance. But you can be assured that it will only be the tourists swimming! The Italians wont go in the water unless its 75 degrees + out (below 60 and they still wear jackets!
If you visit this area make sure you sample:
Limoncello- this area is renown for it... youll quickly realize that.
The pizza- Napoli was the birthplace of pizza as we know it. You can find many antique pizzerias in Napoli's historic district.
Mozzarella di bufala- Mozzarella made from the milk of the water buffalo. This area makes the absolute best, and even have a DOC trademark.
Sfogialtella- a lobster-tail like pastry filled with baked ricotta cheese and semolina
Add to that all the wonderful seafood and pasta (gnocchi alla Sorrentina!!) and its a gastronomical delight!
Enjoy your trip!!