There are roughly a million places to stay in the Mystic area. Here are a few suggestions:

AmeriSuites Mystic	very close (½ mi.).
Best Western	A little longer walk (¾ mi.) to Aquarium.
DaysInn Mystic	½ mile from the Aquarium
EconoLodge	¼ mile from the Aquarium.
Howard Johnson	¼ mile from the Aquarium
Mystic Hilton	Directly across the street from the Aquarium, rock-throwing distance.
Seaport Inn	If you threw your rock over the Hilton, you'd still hit the Aquarium.