My brother ives aboard in the downtown mooring field right now. The waitlist for that field is about six months, although they have temporary moors on the quay wall that are usually open while you wait for a ball. He was able to get on immediately.
The Shelter Island moorings are in the bay and face the open ocean, so they see quite a bit more rocking and rolling than the downtown mooring fields.
Living aboard is certainly tolerated if not allowed; I would estimate that about 15% of the moored boats have live aboards. Cost is right around $200/mo.
Living aboard is a real hassle on a mooring ball however. You're a dinghy
ride away from everything every time, power and sewage are a constant hassle, and the boat moves all the time. It's not something everyone can do.
The least expensive living-aboard you can do in a marina is around $800/mo. as the marinas
all have live-aboard fees
on top of their regular rates, and they're limited to 10% of slips generally. Marina living aboard can be quite nice comparatively.