Bristol is pretty decent in terms of the ski hills in central NY. It has a good variety of runs, a pretty nice lift setup, and a few steeper trails. Plus, it's about the tallest thing in this area of the state (1200 vertical). I was out there once last year while their conditions were okay. They have a pretty decent snow making system, but the lower elevation can really hurt them sometimes in terms of weather (they had a really hard time getting going this season I know).
Nothing in this area of NY is particularly steep though, and you need to keep that in mind. I've also skied Holiday Valley once and personally enjoyed it more than Bristol. It's not a very tall place (only 750 vertical), but it's sprawling, and does have some really nice trails to ski and a really good lift setup to handle the amount of people there. It has a legitimate headwall trail that is extremely short, but a ton of fun to ski down (serviced by its own lift). It's also probably quite a bit closer to you in Ohio.
Just for reference, I usually ski at Greek Peak locally (I have a college student pass for $130 since I'm a graduate student), and go out all over the place to ski otherwise (Catskills, western NY, Vermont).
No matter what, definitely hold off a bit until we get more snow out here. The ski areas are just really getting going with machine made now, and the next few weeks are going to bring a ton of lake effect into the area until the lakes cool down (I heard Ontario is still at 43 degrees which is insane for this time of year).
Hope that helps, and feel free to ask any other questions.
-Craig