Boston has a great transportation system, so you should have no trouble getting around no matter where you stay.  However, if you’d like to be within walking distance of most of Boston’s major attractions there are 3 areas that are best

Boston Waterfront – Aquarium
Copley Square – Theatre District
Quincy Market – Faneuil Hall – Financial

Staying in any of these three areas puts you within 10-15 minute walking distance to attractions like the aquarium, the freedom trail, quincy market and faneuil hall.