The three beach towns eat differently from the rest of Jacksonville, and the rooms worth knowing are mostly about where they sit: on the sand, on the docks, or a block back from the ocean with the door propped open.
Pete's Bar in Neptune Beach holds Duval County's first liquor license after Prohibition, issued in 1933, in a building that was Jensen's Market before that. It has pool tables, it takes cash, and it has never shown the slightest interest in being discovered, which is precisely why it is on this list. A short walk away, The Lemon Bar is on the sand at 2 Lemon St. Several listings still give an old Atlantic Boulevard address. The ocean is a better landmark anyway.
Up at Mayport, Safe Harbor Seafood is a fish market with tables on the working docks. The boats unloading beside you supplied the plate, and no menu can make that claim without the dock to back it up.
If you have kids with you, Flying Iguana in Beaches Town Center and TacoLu off Beach Boulevard are both loud, loose, and big enough that a toddler goes unnoticed. Flying Iguana also runs a tequila list in the hundreds, so the adults are covered.