If they're going to be up for the 4th of July, hit the Esplanade for the fireworks. My advice: Forget the Hatch Shell, you won't get a decent seat unless you're there when they open it (which is like 5am or something) and you won't be able to see the fireworks. Pick out a spot on the Esplanade, bring a boom box for the concert, a blanket, sandwiches and something to drink (alcohol is verboten), and watch the show.
As for bars/clubs:
- The Sunset: 110 beers on tap. Good if you like beer; they don't serve hard liquor though. They'll admit people under 21.
- John Harvard's Brew House in Harvard Sq. They serve their own beer, which is good stuff
On weekends, though, they're usually 21+.
- Cambridge Brewing Company in Kendall Sq. They also serve their own beer. They
never card.
- The Red Hat, near Government Center. Mixed drinks by the pitcher
I especially recommend the mudslides... but don't eat the food.
- Near Fenway Park is a street with a ton of clubs. Some are 21+, others are 21+ some nights and 18+ or 19+ on other nights (call ahead). (ETA: That's where Avalon is. Last I checked, it was strictly 21+.)
Have fun