They don't unlock, they're always there, as are the various services (there's a number of doff contacts and an NPC on the engineering deck that will let you switch to any shuttle). Click the little down arrow at the bottom right corner of the minimap, and then click Visit Bridge. There's a turbolift from there to go to the crew deck and engineering deck. You can change your bridge at the ship tailor, and select from small, medium, and large layouts for the engineering and crew decks. That doesn't change the rooms available or the features in them, only the length of corridors, so generally I go with small to save on walking.
Shuttles all have a single interior, and don't have most of the doff contacts, but they do have an NPC to let you switch back to your previous ship.
Even though I've got a lvl 20 character (just started season 2) , I still feel like a "newb", so here's my question.
At what level do ship interiors unlock?
You can enter your ship interior at any time, though they always default to the Miranda bridge. You can change bridges at the shipyard, and new bridges, the Star Explorer, Diplomat and something else I can't remember unlock as you level up. Those three are basically identical to the Sovereign Bridge pack except for colors, so if you've got an assault cruiser and don't want to spend on a canon bridge pack they're a good alternative.