Can anyone recommend a Boston area hotel that is both close to public transportation (preferably the subway) and that has an airport shuttle? I'd prefer not to pay more than $120 a night, but I'm a bit flexible.
Thanks in advance

Very few Boston hotels offer airport shuttles because the airport is so close -- very accessible by taxi or by public transport (i.e., the Airport stop on the subway's Blue Line). Boston is a very compact town, very few hotels in Boston aren't convenient to the subway system.

Just be careful that the hotel is actually in Boston - not called something like Waltham/Boston or Revere/Boston. Check on various sites that list multiple hotels, and post the names here and I am sure many will have comments about hotel.

Depending on time of year, the $120 may be tough to meet - Boston hotels are very expensive.

But not so tough to meet if you use Priceline!

The fairmont had shuttle to the airport when it was the Copley Plaza, so they may still. That's around the corner from the Copley(back bay ) stop. There's also across and next door from the stop, The Charlesmark, and The Lenox.