I'm thinking about making my first trip to the Boston area, any suggestions on what part of town or suburbs I should stay?

.... you'd like!  ;~)

Seriously, that is probably the most asked question for new visitors to Boston.

In general, in the suburbs it's probably the Burlington area, others can correct me if they feel differently.  In Boston the Copley Place area is generally the area to be, plenty of places to stay with area shopping and dining.

I would suggest downtown, backbay, or cambridge. All have good access and tend to be low-key
looking forward to you visit

Copley, Back Bay, Theater District....you can't go wrong in these areas.  I personally love the Westin, but there are so many good ones there, like Hilton, Sheraton, etc.

with the occasional local LE crackdowns, as has Woburn and supposedly Waltham.  The first two have been verified by a number of sources; the latter from only one source.