The best eating in Halong City is the street food and seafood aimed at Vietnamese visitors rather than international tourists. The waterfront restaurants in Bai Chay tend toward the generic, but the side streets behind the main drag have pho, bun rieu, and bánh mì stalls that open early and close when they run out. If you're staying for any length of time, walk a block back from anything with an English menu and see what you find.
Fresh seafood is the obvious speciality — the local fishing industry operates from Hon Gai, and you'll see the boats from the promenade. Halong crab, squid, and sea snails are all good choices.