In the words of the immortal Gilda Radner, "never mind...."

As Blumie correctly points out in the next post, Suffolk Downs is accessed by public transportation using the blue line, the same line as the airport. Silly, provincial me forgot that there is actually a world beyond the airport (and, in my defense, I did check the Suffolk Downs web site but not the MBTA). My bad, and lots of apologies (and thanks to Blumie for waking me out of my stupor, graciously no less!).

I edited this post to remove the incorrect and misleading parts. I am pretty confident about what remains below, with the caveat that there is actually an airport shuttle bus (Logan Express) to/from Woburn (but you would still want a car).

The rental car locations at Logan are generally very close to Suffolk Downs. On the other hand, you probably do NOT want to have a car in the city as downtown (and to the airport) the public transportation is quite good.

If you do stay in Woburn -- and I agree with what everyone else has said about why that's probably not what you want to do -- then a car is absolutely necessary. However, given the current tunnel mess, transit to/from the airport and to/from Suffolk Downs may be unpleasant unless you know the obscure back routes. I wouldn't expect this to be fully resolved by September, though one can always hope.

Boston's core is very small and easily accessible by T (the subway) or, for those who don't mind a walk, on foot. Woburn is outside that core, and Boston has disturbingly little public transportation outside the core.