I definitely would stay at Chenango Valley state park. I love that park. It's usually very quiet and clean. It's a little bit of a hike to Binghamton for supplies, but you can ride right down the shoulder of Route 81 if you want. You're not supposed to but it's a huge shoulder and I've done it several times and I've seen other bikes on it as well.
Major undulating climbs once you get close to the finger lakes, as you already know.