We recommend you arrive in Boston on Tuesday afternoon (and leave Friday evening). Here are some tips.
If you are planning on flying to Boston, Logan International Airport (BOS) is the closest airport to the city of Boston. A cab from the airport to Back Bay will run you about $30-40 (Ubers and Lyfts will be cheaper—about half that) and the airport is also connected to the city via the MBTA Blue Line and Silver Line.
Amtrak is a great way to travel if you are not too far away. Just be aware Boston has three train stations. North Station is where Amtrak Downeaster trains to New Hampshire and Maine arrive and depart. South Station and Back Bay Station are both served by all other Amtrak trains to and from Boston. South Station is closest to the BCEC, but Back Bay Station may be closer to your hotel.