Freedom Trail is really a must as a Boston experience. Boston as a whole is still one of the most segregated communities, so I'd also be remiss if I didn't encourage you to visit and patronize the businesses in the "lesser traveled" areas; Dorchester, Roxbury, Mattapan (someone already mentioned Darryl's).

As mentioned JFK Museum is pretty nice, a bit further out but worth the trip. Of the other museums, Isabella Stewart Gardner gets my vote.

Castle Island (not actually an island) for a lovely walk by the water.

The Boston Harbor Islands (actual islands) are also great for a day-trip.