If by any chance you are not talking about going to the city, the rest of New York state has plenty of natural beauty. We visited the Finger Lakes region, Letchworth State Park, Watkin's Glen and the Cornell Campus one time, as well as the Erie shoreline and canal and Niagara Falls. There is a notable wine region. We were there in autumn, so I can't say what May would be like, but I imagine it's pretty comfortable, and not overly crowded anywhere before school is out. We didn't have time to see the Catskills and Lake Champlain on that trip, but of course that would be worth seeing, also.
One of the weirdest travel experiences we've ever had happened in one of the small towns on that trip. Sorry, I can't remember which (maybe DH can, but he's asleep). We checked into an ordinary motel near the main hwy, and were roused from sleep at 2:00 AM by the civil defense siren blasting very nearby. This was only a couple of years after 9/11, and it scared the $%& out of us. We looked out the window and saw nothing but a beautiful, serene night with clear weather. Finally I called the front desk and was told, "Oh, that was just the monthly test." This was in an area where there were at least 3-4 motels, and did I mention it was extremely LOUD?!!! What were they thinking? The people who made that decision clearly had it in for tourists and motel owners. I wish I could remember the name of the place. We would never go back to that town, but the rest of NY State was exceptionally nice, as far as we could see.