Staying in Siena

sg,

A few thoughts on your questions......

1. Touring hill towns is one situation where a rental car is an advantage, however that depends to some extent on exactly which places you plan on visiting. There are a few potentially expensive "caveats" to keep in mind with driving in Italy such as the fact that each driver will require the compulsory International Driver's Permit, and you'll also have to be vigilant to avoid the dreaded ZTL (limited traffic) areas in each town, as hefty fines will result if you pass through them.
2. That's difficult to say, as the everyone has different interests. A city that one person finds interesting may not be as attractive to the next person. I'd highly recommend buying a copy of the RS Italy guidebook and looking through the list of cities and deciding which ones look best to you.
3. If you're renting a car, somewhere that provides parking! Finding parking is often challenging in Siena, so if you're renting a car that's an important consideration. The guidebook has information on good accommodations in that area as well.

If you're only going to be in Siena for two nights, I'd highly recommend leaving some time for Siena as well, as there are some interesting sights there. Two nights will only provide one full day of touring so you'll have to prioritize. If possible you might want to add a night to Siena.

On our RS Best of Italy Tour, we stayed at the Hotel Chiusarelli. We had a nice room at the back of the hotel. If you were to book a room there, be sure to ask for a room in the back. I would stay there again if I visit Siena again.

While in Siena you don't need a car but if you want to explore surrounding areas during the day a car is best. I stayed in Siena three nights and picked up a car the second day which left the first day to explore Siena. Staying just outside the walls we were able to park at our hotel and easily arrive by train. Hotel Italia was close enough to walk to the center of town and easily accessible to the train station and car rental agencies. If you arrive by bus you will be dropped in the center of town which wasn't ideal for my logistics. We toured Chianti to the North on our first day of car rental and returned to Siena before dark. When we left Siena by car we stopped at several hill towns, over nighted in Montepulciano before dropping the car in Orvieto where we stayed for two night before taking the train to Rome. The logistics of that itinerary worked out very well. Driving through Tuscany is amazing and exceeded my expectations. A GPS that I brought from home made the driving easy.

Hotel Italia if you want to be close to the station, which is about 25mins walk to the centre.
http://www.hotelitalia-siena.it/en/

When in Siena, I always stay at Albergo Bernini. It is very close to a bus stop and St. Catherines church. Has a fantastic view of the duomo from their terrace.

sg,

I'd also recommend Albergo Bernini in Siena, although I don't believe they offer parking.