Don't know what you enjoy, but if ice cream is your thing, New England is the ice cream capital of the world, and there are lots I'd highly recommend: Christina's, Herrel's, Toscanini's, Coldstone Creamery, Emack and Bolio, maybe JP Licks. Yesterday, I had the most fabulous sweet cream ice cream with caramel, fudge, and pecans, smushed in using paddles on a marble countertop at a newly opened Coldstone Creamery... Mmmmm...
Duck tours are fun. I was amused that some neighborhoods became quack-free zones, I guess after the tour participants quacked too vigorously. Walk the freedom trail. Visit the USS Constitution or Bunker Hill.
If you like the book Make way for ducklings, you could always visit the Boston Public Garden, ride the swan boats, watch the kids sit on the duckling statues, stroll around past the state house, and into downtown.
Get a canolli and cappucino in the North End (dang it, I can't remember the place's name).
Wander around Harvard Square on a Sat night; in June, there's bound to be great people watching and performers out.
If you have a rental car, go out and visit Walden Pond. Beautiful place.
The Children's Museum is fun, as is the Museum of Science. If you are feeling more learned, you could always go to the MFA (Museum of Fine Arts) or the Isabella Stewart Gardner museum. Harvard has a couple dozen museums; it's neat to see the glass flower museum out there (back when botanists would model their flowers with glass, because pressed specimens didn't last, and sketches weren't enough).
Oh, and did I mention ice cream?
That should give you a start!
(I think I'm the only person responding with less than 1,000 posts. Am I still allowed to post here? I suffer from post envy...)