Universal Hub‘s Adam Gaffin has created a database of places in Boston that are open 24 hours a day. The North End/Waterfront area only has one listing – Bova’s Bakery at 134 Salem Street.
After that, the closest are the Dunkin’ Donuts on Causeway St. by the TD Garden and Tedeshi on State St., which I believe is/was a Store24. Charlestown has the all-night Shell Station and another Store24. There are none in Beacon Hill, while the Back Bay has Shaw’s and a Store24. The Leather District has the South Street Diner and The News. Click the map below to go to the Boston 24 website.