Since this is posted under the Supply Officer portion of the website, I can only assume you are either a Supply Officer or a prospective one. On the carrier, Supply Department runs the operation for officers' staterooms. What this means is that if you are going to be a supply offier and are heading to a carrier, you will most likely already have an "in" into the system. Not always, but there is a good chance. There is also that possibility that it could be you who is responsible for the staterooms (there's more to that division than just that though). So in theory, you could be assigning your own stateroom to yourself. In any case, the goal is always to keep all the aviation bubbas up near flight deck since they're the ones making all the rackett and ship's company (even if they are aviators) as low in the ship as possible (if that's what they want of course). My recommendation to you is to find a room on the second deck (people are ALWAYS checking in/out on a carrier so a room is bound to open up quickly if not readily available), as close to centerline as possible, in the aft part of the ship (cause that's where the main wardroom is).
On a small boy, you're gonna be the fng and will most likely wind up in 6 man at best, and overflow berthing down below at worst....at least until you have some time onboard. The quality of stateroom you get on a small boy will be very much a function of how long you've been onboard, senority, and respect from the other JO's. If you let the other JO's walk all over you because you're a supply type, they'll eat you alive and you'll be in 6-man for your entirety. Don't put up with it. As the Suppo on a small boy (we're talking DH billet now), life is good. Depending on the type of ship (Frigate, DDG, CG) you may even have your own stateroom....typically that is on a CG.