Kingdom Hearts Wiki page for The Castle That Never Was
Aside from all the areas listed in the article, one can assume that the castle also has bathrooms (most likely attached to the bedrooms), a kitchen, a dining area, and general storage areas/broom closets/what have you. These can be handwaved in as needed. Also, the area known as 'Where Nothing Gathers' or just 'The Round Room' has no windows or doors and cannot be accessed except by teleportation.
Only the force-fieldish energy bridge leading up to Nothing's Call actually touches the ground. The rest of the castle will be hovering about 50 feet above the ground.
Axel will be living there alone for the time being, but will eventually be opening up some of the Castle's rooms to anybody who needs a place to stay and doesn't mind living in a somewhat creepy floating castle full of Nobody symbol sigil-spam. Rooms #13 and #14 will remain reserved for Roxas and Xion, respectively, if they ever arrive in the City and wish to stay there. Other Organization members may also try to claim their old rooms if they arrive there, of course, but if someone else has already claimed it by then, they'll have to fight for it or find somewhere else to stay. Axel's only reserving rooms for his friend Roxas and (though he can't remember her and thus doesn't know exactly why he's reserving that extra room) his friend Xion.
Current room listings are as follows:
#13: (Reserved for Roxas)
#14: (Reserved for Xion)