I'm just going to be there for around 21 hours, fly in on Saturday morning, get the rental car, drive around and see some sights in the afternoon, go see a concert in the evening at the FleetBoston center/place, and then catch an early bird flight home (which means I'd be returning the rental around 4 a.m. or earlier if I just hang out at the airport during the evening (the hotel rates are pretty high).
If you're just planning on seeing sights in the city I'd highly recommend against a car. You can take the T (subway) for $1.25 to the center of town and it's pretty quick. Or you can take a cab for ~$20 or so. With the rental plus $20+ for parking you should save money, and save your sanity.
You can't really drive between the sights here anyway, and, except on the main roads, all the parking is restricted to residents w/ stickers only (you will get a ticket!), except for paid lots, obviously. So, if you're up for a few miles walking, you can see the entire center of the city in an afternoon.
If you want a good, cheap, place to eat go to Pizzeria Regina while you're here. It's a landmark and is the best pizza in Boston. Also, it's only a few minutes walk to the FleetCenter, and it's in the North End (the 'old' section of Boston) which is a great place you should stroll through anyway.
I flew in for a couple days just for a concert once too.
The only reason I was thinking about the car rental was more for the "locker" aspect of keeping my stuff (change of clothing, camera, etc) in a car, versus lugging it around for a day (and into the concert).
Pat, I agree w/Bill's recommendation against renting a car in Boston. Driving is brutal "in town" (as we call it) for us, nevermind for someone not familiar w/the area. I'd hate to see you waste half your time here sitting in traffic and looking for parking. As for the Pizza recomendation, Santarpios Pizza in East Boston (a stone's throw from Logan) has better pizza than Regina.
Bill, I think the concert Pat is going to is probably at the FleetBoston Pavilion (formerly Harborlights) not at the FleetCenter. Most of the spring/summer concerts in or around Boston are held there or at the Tweeter Center.
Boston traffic has been bad from 1954 to the present day, all days inclusive. You really cannot explain it to someone who has never experienced it. Take 1 million people in cars, put them on cobblestone roads (mostly one way) made 250 years ago for horses and cows, instill in them the most cut-throat, aggressive and dog eat dog driving skills in the world, then let them loose. Trust me, take a backpack, rent a locker at the airport or rent a room. All will be cheaper (expect maybe the room) and all will definitely be safer and less frustrating to the uninitiated. Boston is real easy by 'T' or by Taxi, both are reasonable, with a 'T' all day pass being the best bet. Visit MBTA.COM for everything 'T'.
However, if you are just going to the Pavillion (not the Fleet Center, big difference) and parking, renting may be OK. Go here for directions from Logan:
As a non-Bostonian who's visited the city on several occasions, I wholeheartedly agree with the recommendation to avoid driving in Boston. I had a car there once, and used public transportation the other times. The city is much more enjoyable if you do not have to drive, between the traffic, lack of parking and confusing navigation. You can take a taxi or shuttle from Logan Airport, and the subway will get you close to most of the main areas. It's also a great city for walking.
Speaking of Beantown, if you want the quintessential Boston food experience, go to Durgin Park in the Faneuil Hall Marketplace. Faneuil Hall (or Quincy Market, it's called both) is the biggest tourist attraction in Boston and a must visit for first timers. Durgin Park is one of the oldest eateries in the country. The food is good New England family fare (pot roast, turkey dinner, baked beans, the worlds best cornbread, indian pudding, brown bread) and the service is uhhhm . . . uniquely Bostonian. Do not be put off by the austere surroundings (the rags tied around the pipes in the ceiling, for instance) and don't be put off if they make you sit with strangers, the food is great and worth the wait. Grab a beanpot (with great recipes) in the giftshop on the way out.