Davis Sq has been my stomping grounds for the last 7 years or so. There are some great restaurants in addition to the aforementioned Redbones.
Painted Burro has great Mexican & margs
The Foundry is a gastropub w/ pretty good craft beer and whisky selection
5 Horses is fairly similar to The Foundry but a little more mainstream and a bit cheaper. Better Beer list in my opinion.
Next to the Burren is an unmarked door that leads down to Saloon. Its a great whisky bar. Neat vibe.
Harvard Sq is also worth checking out for restaurants and bars.
For touristy things - I would have to agree with
@Jay-Bone that the Duck Boat tours were much better than expected.
Something I did recently that I really liked was a Boston Harbor Cruise to Spectacle Island & George's Island -
Harbor Islands
Spectacle Island has a very easy hike that will get you a nice view of Boston, and Georges Island is basically an old fort. Very cool to explore. You can even bring food out there and they have grills and pick nick tables set up. Only costs $17 for a round trip ticket and you can plan your own day based on their schedules.
The Gardner Museum is my favorite in Boston.