I used to live in Bay Shore and thoroughly enjoyed the bays in a
32-footer that drew 3 feet. There are some really nifty places to
explore -- Sunken Forest at Sailor's Haven on Fire Island, and many
other Fire Island towns. With 4 feet you'll have to be more than
judicious and VERY motivated to do it, but by watching the channels
and timing your travel to the tides, you should be OK. You WILL
ground, but usually in soft sand. One trick, at least for seeing the
Fire Island towns, is to come in the Fire Island Inlet (slack tide is
best!), make your way to a berth in one of the Fire Island towns, and
use the water taxi service or the ferries that regularly cross the bay
from the mainland (Bay Shore, Sayville and Patchogue all have ferries
going to the different towns) to see the sights, such as they are.
BTW, the ferries are big boats that all draw at least 3 or 4, maybe 5
feet. They stay in the channels.

Further East, the bays get VERY shoal, and only local knowledge will
get you through. Moriches Inlet is used by locals, but is
treacherously shoal; ditto for Shinnecock. Nonetheless, local sports
fishing guys use them routinely, because they know the shifts, which
are frequent. All of this being said, I haven't been boating there in
several years, ahving moved to Atlanta 25 years ago. Last time I was
out on the bay I was eastbound from Lindenhurst to Bay shore in a 36
foot Chris Craft, and fetched bottom twice. No harm done, beyond my
ego and a little fragility added to my friendship with the guy whose
boat I was using.

Plan well and go for it. Then go thru the Shinnecock canal (much
argument here if there's a lock or a gate; if you go, please edify us
all) up into the Peconics. Stay in Sag Harbor for a little while, go
around to Greenport for a couple days, and anchor in Deering or
Coecles Harbor and rent a bike on Shelter Island. From there run out
to Montauk, thence to Block Island. All really great places.

Also, for an unusual cruising break: if you stay over on Fire Island,
ferry over to the mainland and take the Long Island Railroad into
Manhattan for dinner and a show. An hour and a half each way, but
what a neat juxtaposition to a cruise. We used to stay at Atlantique
on Fire Island from Thursday night until Monday night during the
summer months, and I'd commute to my office in New York on Friday
mornings while my wife and kids enjoyed the beach.

It's skinny water, but not too skinny for 4 feet.