May in the finger lakes can be chilly but we like this time of year since kids are still in school and the parks are not busting at the seams.
Letchworth State Park is beautiful, the RV sites at the state park are small though but they do have electrical hookups.
We stayed at Woodstream RV park once, family owned, lots of seasonal sites which we don't care for but it's reasonably priced. Not far from the state park but then you pay daily access fees each day you enter the park.
Another great trip is Watkins Glen, the KOA is awsome if you have kids. Much more activities in and around The Glen than Letchworth.
Each park has its pluses and minuses depending on the age of your family and what it is everyone likes to do. Some of the state park sites at Watkins have electric as well.