If you're staying at a hotel near the convention center and need a way to get from the airport to your hotel, I suggest taking the subway. There is a complimentary shuttle at the airport that will take you to the MTBA Airport Station. At the station, you want to take the Blue Line (Inbound) until you get to Government Center Station - To Bowdoin. Get off here and catch the Government Center Station Green Line W and get off at the Hynes Station. Hynes station is a short walk away from the convention center and surrounding hotels.
I've called some cab companies and the usual fee is about 20 dollars from the airport to this part of town. The train is 2 dollars.