Standard Bakery has great loose-leaf tea and baked goods and is a great place to grab something quick.
Micucci is the local Italian market - drop in for take-out Sicilian pizza.
If you'd like fancier, dine-in Sicilian pizza, Slab is incredible.
Uncharted is a bubble tea cafe with seating, games, and unique drinks.
I haven't been as it's not veggie-friendly, but friends and passengers raved about Duck Fat.
Fort Gorges is open to the public but only accessible by water taxi. Suggestion: pick up breakfast from Standard and go first thing on Sunday morning.
For coffee, I like Bluestone Lane Harvard Square Cafe and Blue Bottle Coffee (often busy), both in Cambridge.
Visit Newbury Street for Japanese standards Uniqlo and MUJI. I am informed that Rooted In (also on Newbery) is a great place for weed. For books, Cambridge is my favorite spot - I love the Harvard Bookstore and the Harvard Coop, and the MIT Press store is next on my "to visit" list. Barbara's Books (in South Street Station) and Trident Booksellers (a cafe / indie bookstore on Newbury street) are worth a stop. If you're in Chinatown, Morefun is a cute Asian giftstore.
For quick bites, Tatte is good but a bit pricey, and I like Clover as well. Quincy Market and Boston Public Market both have a wealth of quick options (of varying qualities.)
I like State Street Provisions and Alden and Harlow for cozy upscale American, North Street Grill for a diner, and Lucy Ethiopian for, well, Ethiopian. Lone Star Taco Bar has great tacos, affordable mocktails, fantastic chips, and incredibly quick service. In Chinatown, check out Taiwan Cafe (suggested by my Taiwanese friends, staff was very patient with my rusty Mandarin but with a full English menu).
My favorite bubble tea is Gongcha, but Kung Fu Tea, while not unique to Boston, is also a good choice. Teazzi is nice if you like fancier, fruitier options.
Boston has some incredible museums - I love the Museum of Science, the Harvard Museum of Natural History, the Museum of Fine Arts, and the Isabella Stewart Gardner Museum. If you're interested in medical history, MassGeneral has a small, free medical history museum as well as a sometimes-open historic opperating theater. Liberty Fleet, a former employer of mine, does nice daysails on the harbor during the summer season. The U.S.S. Constitution is a neat visit. I've heard that Boda Borg, a sort of challenge center/escape room, is great fun, and I can attest that Level99, a different sort of challenge center/escape room, is also a blast. (It's also in a very nice mall.)
Speed round while I pull together actual lists for other spots: Old Professor's Bookstore in Belfast, Maine and Bar One and Union Coffee in Milford, NH.