Historical stuff, the obvious thing is the Freedom Trail if you want to do some walking. Literally a red line painted on the ground that you follow that takes you past many of the historical landmarks starting by the Boston Common and ending in Charlestown at Bunker Hill. You see places like the Old North Church, a few old cemeteries, some other historical buildings and the Constitution (though I think the Constitution may be out for repairs and not in dock this summer).
Weird/nerdy vibe sounds like a trip to Harvard Square might be worth your while. Bunch of different style shops/bookstores, all walks of life for people watching, if you like burgers try Mr & Mrs. Bartley's Hamburgers on Mass Ave in Harvard Sq., if you like Tex Mex, try The Border Cafe on Church Street (kind of a shit hole decorum wise but good food).
Other popular tourist things include the duck boat tours which are the amphibious vehicles which take you around the city then go into the Charles River. Museums and the Aquarium if you're into that, as well as whale watching trips (they depart from the Aquarium).
Pleanty of restaurant options. Can't swing a dead cat in the North End without hitting a small Italian Restaurant. Chinatown of course has various levels of hole in the wall Chinese places.
Seaport district has been recently revitalized and some restaurants there including a Legal Seafoods (also one in Park Sq), The No Name, The Daily Catch and a bunch of others...most of these in this area a bit pricey.
Fanueil Hall has places to eat and overpriced places to shop, as well as a big food court type building with dozens of options.
And of course a favorite for New Yorkers is Fenway Park for a game or they do tours if the Sox are out of town.