We will be in Italy the first week in April.
We stay in Florence for three nights, move on to Sienna for 2 nights, then back to Florence for one night, leave the next day.
Should we rent a car? Should we stay the last night in Sienna and try to get to the Florence Airport the next a.m.?

You only want a car in Siena if you will be going on to other towns.
There's no point or need to having it if you are staying in Siena, and you have to park outside of the city center.
Easiest transport between Florence and Siena is by bus. Train is longer,requires a change, and train station is outside city center.

I would not recommend driving from one city to another on the day I have a flight--too many things can go wrong.
How about staying in Siena first, then spending the several days in Florence and leave from there. Saves the time lost in back and forth, and Florence airport is only about 20 minutes from Florence center, at least without traffic problems.

I agree withe ELaine. A car is only another thing to worry about if you are not going to visit other towns. That being said, perhaps you want to get a one day rental and drive from Florence through Chianti to Siena and then drop if off in Siena. It's a gorgeous drive. There is also an American cemetary just outside Florence that is incredibly moving.

Thank you for your comments.

Unfortunately, we have already paid for the hotels in both Florence and Siena, and the reservations can't be changed. Can we visit by bus or train some nearby towns from either city?

here are some random suggestions

www.annells.demon.co.uk/main/busita.htm links to websites on Italian bus services

http://150.217.9.3/ie/citybus.htm
bus service in selected cities in Italy

www.tiac.net/users/pendini/bus.html bus service, Florence airport-train station, & to Siena

from Florence to San Gimignano: The best route is by bus via Poggibonsi, where you will normally have to change. When you get off at the transfer point, walk across the street to wait a few minutes for your next bus. Travel time depends on the connection there, but is normally about 1.5 hours.
You can find timetables here:
http://www.comune.poggibonsi.si.it/citta/giro2/
Bus at San G. will let you off right at the town gate.

Recommended by Rick Steves and in International Travel News Aug 03: Tours by Roberto, c/o Patricia Bechi, Via del Forno, Vecchio 14, Serre de Rapolano phone/fax 039 0577 704789, www.toursbyroberto.com
Office located just outside Siena. Roberto Bechi is fluent in English. He does day-long trips (food, culture, wine) in the countryside around Siena, and his assistant does half-day tours of Siena.

Busses will allow you to go virtually anywhere. For example, look at:

http://www.trainspa.it/
http://www.turismoverde.com/italia/trasport/bus.htm

Thank you all for your help.