I sail out of Mt. Sinai, NY, the same basic waters as you.
Your budget is going to restrict you to older boats. Nothing wrong with that, but still....
I would look for something smaller, like in the 27-30' range. Back in 2004 I was looking to move from a Catalina 22 to something around 30'. I found that 27-28' boats were a lot cheaper than 30-32' boats. For the same money, you can get a nicer 28', or you can get a comparable boat for less money.
The waters we sail in can be benign, or they can be real rough (especially in May and October). If you really want to go out on those rough days, buy a heavier boat. If you would rather stay home on those days, and sail in July and August, buy a lighter boat.
The Catalina 30 would be a great choice. That was #1 on my list when I wanted to move up. I ended up with a Newport 28, which I was very happy with. Compared to a Catalina 30, the Newport was nicer below (teak and holly sole, leaded glass cabinet doors, padded headliner, etc. The Catalina has lots more room below, but for 2 people, the Newport has more than enough room. I'm not trying to sell you on Newport, just try and note the differences between boats. The galley on the Newport was small, but that is true on almost all boats below 35'.
FYI, I looked at a Islander Bahama 30 - same basic boat as the Catalina, but on this one, the deck was all rotten around the main hatch
Some other boats you should look at are the O'day 30 and 31. If you can find an O'day 31 they are very nice because they have a small swim platform that makes getting on / off the boat from the water or dingy very easy. I would not recommend the O'day 34 because one in your price range would be in poor condition.
If you can find an older Tartan or Sabre 28-30, they are very nice boats.
Actually, there are many boats out there, including Pearson, C&C (more racy, not as stable), Cal, Ericcson, etc.