I went for the massive, modular space ship option, though the options aren't necessarily mutually exclusive. Massive, modular, vortex traversing space ships could be tesseracts or central spires or disjoint rooms linked dimensionally.
I hadn't really considered what the TARDIS "looks like" - not sure the question means anything, given the "inside is bigger than the outside" thing.
So, does the TARDIS actually "go anywhere", or just the blue box?
the blue box is moved, which then moves the ship (it's 4th dimensional form) about the universe.. because the ship's interior is outside of our dimension of space/time, it can open a doorway at any point in space and time to itself..