Not sure where in Boston you are, but just make sure you get out of / do not enter downtown Boston or the Northeastern/BU/Wentworth cluster. There are recommendations here for the North End (crazy touristy), the Greenway (touristy, hot, and boring), the freedom trail (really?). Yuck. The MFA and Gardener museums are good but surrounded by undergrad garbage. Sorry for all the hate, but I feel like I fit your description and I'd be disappointed with Boston on that tour.
My top two recommendations:
Davis Square, on the redline. There are at least four fro yo shops within two blocks, so you can take your pic. Also Diesel Cafe - good coffee, food, and they always have local artists featured on the walls. There's a bike path in the area if you want to walk around. There's also a movie theatre with a "bad art museum" in the basement. (Don't go to Davis for the museum - it's a goofy novelty - but if you go for the fro yo and Diesel, it's worth a look. No ticket required.)
Jamaica Plain (JP) especially around Centre St and Green St. 10 minute walk from the Green St or Forest Hills stops on the orange line. My favorite JP hipster cafe, City Feed & Supply, plus tons of other good places for food including the ~original~ JP licks and a vegan icecream place (FoMu). Lots of second-hand stores - Goodwill (boring), Boomerangs (best), 40 South St - and some little art stores. Also a short walk from the Arnold Arboretum and Jamaica Pond, which are both beautiful.
Runners up:
Harvard Square, red line. Lots of cafes, bars, shopping, night life. You can actually take the T to Harvard and then walk all the way down Mass Ave back to Boston - you'll go through Harvard and MIT as well as a bunch of interesting stuff on the way. Toscanini's at Central Sq for coffee and ice cream. The MIT museum is cheap and fun.
Union Square. Cute working class neighborhood transitioning to "hipster paradise" (quote, my professor). The trouble with this is it's awkward to get to. You'd probably have to take a bus (unreliable). But I like Bloc 11 cafe and Union Square Doughnuts are always a good souvenir. There's also the Artisans' Asylum, Brooklyn Boulders, Aeronaut Brewery complex to check out.
Coolidge Corner, Broookline (green line, ugh). Paris creperie, JP licks, Brookline Booksmith, etc
South End along Tremont Street. Amazing food, very yuppie/WASPy/expensive. Some cute boutiquey stores.
Alston. Dirty hipsters / frat bros. Great dive bars, great food, and its kind of becoming a second Chinatown in my experience. Lots of good asian food (so many bubble tea cafes) and asian karaoke.