Well the good news is the entrance to Shinnecock Inlet was dredged over the winter. The bad news is its still tricky if there. Likely to still be breaking waves if there is any swell. Wind against current makes for interesting conditions too (the current runs through there at a few knots) so slack tide is advisable. If its calm, you should be fine.
Once your in Shinnecock Bay, it is imperative that you stick to the marked channels. Shinnecock is really shallow! In terms of where to stay, your best bet is probably Jacksons Marina which is just on the other side of the bay relative to the inlet. If fact, if you give them a call and ask to speak to Mr. Gordon Jackson, he will give you the lowdown on the inlet. He's and old sailing salt with lots of local knowledge and nice enough that he would chat with you about it.
Anyway here are some links...
Hampton Bays News - Workers finish dredging Shinnecock Inlet; project comes in $3 million under budget - 27east
Sea Conditions at Shinnecock Inlet, Long Island, New York USA
Jackson's Marina Enterprises Inc.