I always had mixed feelings about the torpedo bays on the refit Enterprise seen in TMP, but you have to admit that if there were any torpedo banks outside of the lower saucer decks, even the minimalist neck of the TOS Enterprise would be a great place to house at least one of them... and "Balance of Terror" seemed to suggest there were forward weapons, mid-ship weapons, and aft weapons on the Enterprise.
Beyond the notion of at least one torpedo facility, there are a few other possibilities:
- an observation lounge
- fabrication facilities (In "Catspaw", Kirk told Korob his ship "could manufacture a ton" of the precious gems)
- an airlock/travel pod port
- other permanent equipment, such as sensors
- piping and wiring conduits between the hulls
- turboshaft, of course
None of this is canon, of course, but canon pretty much ignored the neck anyway. If we retcon from TNG, though, we can assume the neck is used for some kind of ship's facilities.