As for fun, just touring the Quincy Market area is fun, especially if you like to shop.  The Aquarium and its I-Max is not too far, and there are boat excursions from around there.

If the ocean gets you a bit seasick, then head up to the Public Gardens and take a swan boat ride.

Financial District, shopping not that great, if you coming on a weekend, all your going to hear is crickets.
Quincy Market is a tourist trap, you, need to hit Newbury street (still a little bit of a tourist trap).

Also see post about Boston Food: http://www.theeroticreview.com/discussion_boards/viewmsg.asp?MessageID=153549&boardID=9&page=1

For Food:

O Ya (pricey but very good)
http://www.oyarestaurantboston.com/menu_dinner.html

Radius
http://www.radiusrestaurant.com/

Les Zygomates (they have Jazz bands)
www.winebar.com


Sam La Grassa's (great sandwiches)
www.samlagrassas.com

Silvertone Bar & Grill
www.silvertonedowntown.com

For Coffee:

Espresso Love
http://www.espressolove.com/


Night life:

Revolution Rock Bar
www.revolutionrockbar.com



.

If you're on Newbury, there are two places near the bottom of the street (away from financial district) that are pretty good.

Espresso Royale Cafe, 286 Newbury - www.espressoroyaleboston.com, which also has a location on Comm Ave closer to the Common.

Wired Puppy, 250 Newbury - www.wiredpuppy.com