Rob,
Was just there a few weeks ago with Dave and Walter. The aquarium is inland so there isn't anything "next" to it. You can get close to or stay at the Seaport which is probably a long walk or a short cab ride away.
We stayed at Mystic River Marina which was ok but not close to anything. $10 cab rides to go anywhere. Since it was my first time there, I can't give a recommendation on any of the marinas that are closer to the Seaport.
We usually make Montauk a stop on the way out there or on the way back.