I live and work here and people ask me all the time what should we do when in Boston. And I always laugh because I'm here everyday and can't think of cool stuff to do since I don't think about what it's like to be a tourist here. I think of Boston in neighborhoods. Neighborhoods you want to check out are Back Bay, Beacon Hill, North End and South End. South Boston also if you have time. Try to do something in each of these neighborhoods. Boston is pretty small so it's easy to walk everywhere or take 5-10 minute Uber rides.
Touristy things - Besides things already mentioned I always thought the
Duck Tour was kind of cool. Easy to way to see the entire city in a few hours. Leaves from Back Bay (Prudential Center), downtown (at the New England Aquarium) or Cambridge (at Museum of Science).
Beer - Trillium has great beer but instead of going to the brewery in the Seaport go to the
Trillium Beer Garden on the Greenway downtown. Closed Monday and Tuesday so probably won't work for you. Close to North End so you can combine that with a beer or two before or after dinner in the North End. The
Trillium brewery in the Seaport is also fun and that is open everyday (and serves lunch and dinner).
Food - Here are some options in different neighborhoods.
North End - There are so many good ones. Lots have outdoor seating if it's nice out.
Arya Trattoria is very good but it's on the 2nd floor so no outside seating.
Carmelina's is good also and has an outside seating area. Get a cannoli at Mike's or Modern Pastry. Both on Hanover Street and both always packed. If you like pizza walk over to Regina Pizzeria at 11 1/2 Thacher Street. Known as the best pizza in Boston.
South End -
SRV is one of my favorites. Then walk over to the
South End Buttery for dessert and sit outside on the bench and people watch.
Back Bay -
Stephanie's has good, not great, food but the outdoor deck is the best people watching place. On Newbury Street.
Grill 23 for steaks (expensive).
Beacon Hill -
Peregrine and
Scampo are both very good if you want to check out this area. Grab an ice cream at
J.P. Licks and then walk down Charles Street, the most authentic old Boston retail street in the city. No chains here.
South Boston - I like
Fox and the Knife. Kind of a hard neighborhood to get to from where you're staying. Too far to walk. Broadway T stop on the red line is right across the street from this restaurant.