The Navy doesn’t run live-fire exercises in one of the most traveled shipping channels and commercial and general aviation areas in the country that is the Long Island Sound.
The vast majority of Navy missile tests that are conducted in (contiguous) US territorial and adjacent waters are in Point Magu on the west coast and White Sands, also on the west coast. I believe the only active missile test range on the east coast is located in Florida, the Eastern Test Range which is at Cape Canaveral. The Atlantic Test Range, located off the coast of Virginia, was once used as a missile test range. But, I’m not sure if it still is an active missile range (although it certainly hosts other live-fire tests).
The FBI doesn't file doctored evidence to obtain FISA warrants, either. :-P