There is so much to see in Tuscany it's hard to know where to begin. Any of the hilltowns are great. If you have the apartment for the entire time, you can do day trips to lots of places. And not just in Tuscany. You can go to the Cinque Terre from there, and many other places. I wouldn't bother renting other places for night stays if you have this apt for the entire time. You'll be in a great jumping-off place for other locales.
In 2003 we rented an apartment in Montepulciano. It was up on the top (3rd) floor, and had 2.5 floors itself. The view from the rooftop balcony was of the hills to the south and east. I told my wife she could kill me now, because life would never get better.
I'm so envious. Can I come?
I'd say have a great trip, but a great trip in ensured.