Welcome to Boston!
North End recommendations.... Ristorante Saraceno on Hanover St. Delicious and Authentic...not a tourist trap.
La Galleria 33 on Salem was just overhauled by Gordon Ramsey. I havent been, but heard its good. Its on Salem St. Save room for Bova's bakery for dessert! YUMMMMMMMY!
Here is a list of events for the 4th....
http://www.bostonusa.com/harborfest/schedule/
I personally like the waterfront area and boat venues. Harbor cruises, Sailing, whale watches, deep sea fishing etc, Take a ferry to Georges island, Gloucester, Cherlestown or Provincetown for the day. Lots to do at each (well..maybe not Georges..old fort to look around. Kind of boring..)
Salem, MA is close by. Old witch town with witch museums & haunted tours..nice day trip.
Rockport, MA. is also close. Beach, sightseeing, shopping, restaurants, outdoor entertainment. LOVELY area, lots to do for the day.
If your beside the common, you must know about the theatre district. There are day of, 1/2 price ticket kiosks throughout the city. Purchase your ticket same day and get 1/2 off.
Improv (comedy show) on Hanover (north end) is fun.
Red Sox game? !!
Mohegan Sun Casino in Uncasville, CT. About 1.5 hour drive. Lots of shopping, restaurants, free nightly concerts and GAMBLING!
Cape Cod (though if your going on the weekend, go very early as traffic gets terrible after 8am. Hyannis / Hyannisport is my favorite area. Lots of water activities, entertainment, shopping, restaurants up and down Main St and the marina is within walking distance. Without traffic, its about a 45 minute drive.
If youre staying at a hotel, ask your concierge for recommendations.
Enjoy your stay!