Definitely get one of the Long Island Sound Guide Books, also a copy of
Eldridge would be a good idea. There are a number of fine ports on both sides
of the sound and at both ends. While the sound is not very big, less than a 20
hour run from on end to the other for even a slow boat, I suggest you carry a
cell phone as well as the usual VHF and call ahead for marina reservations
regardless of were you are. There are few good anchorages anywhere in LIS.

If you are secure in your navigation consider a run through the Thimbles.
Essex, a few miles up the Connecticut River, is a must. If you have the time,
you might want to spend a night anchored in Hamburg Cove.

After Essex, you can consider crossing over into the "forks" of Long Island. A
trip from Greenport around Shelter Island with stops at 3 mile, Sag Harbor, and
maybe one or another would be a great way to spend a few days. You might want
to end up at Montauk. By the way, most of this area is called Gardner's Bay,
not LIS.

You need to time your passage from Essex to Greenport to hit slack at Plum Gut,
and you should have reasonable favorable weather.

After this "circumnavigation" I would leave Montauk and cross over to Block
Island.
You will definitely note that you are not in the sound now, but in the ocean,
with ocean swells, etc. So wait for good weather. Go for the inlet at Great
Salt Pond. Moorings there are first come first serve. Dock space is by
reservation, and anchoring is limited. If you anchor, have good heavy gear,
and make sure it is well "stuck." If you want dockside, call now for a
reservation!

After Block, I would take a run across Block Island Sound, through Watch Hill
Passage into Fisher Island Sound. ( If I had the time, I might consider east
and spending a few days in Newport, etc., but you said LIS.)

Once in Fisher Island Sound go up the Mystic River. If you have reservations,
or can get dockside at Mystic Seaport Museum, fine; otherwise, there are two or
three fine marinas NORTH of the RR bridge right in downtown Mystic. Not a bad
walk to the museum or the restaurants.

Heading back west from Mystic, you can go back into LIS from Fisher Sound and
stop at all the places you missed on the way east.

LIS is always crowed, usually cold early in the season, then hot and muggy with
possible afternoon thunderstorms in July and August. It can get foggy as you
go east. To me the best cruising is just after Labor Day until early October.
Navigation is easy: East & West go up and down sound, North and South bump into
land! :-)