I've been to LP several times. Given the area, you'd think there would be amazing mountain biking, but it's actually quite limited. I know there are a lot of trails, but a lot of them are "technically illegal", so the locals won't advertise them. I did an Xterra race a few years ago up there, and a good portion of the course was on private land I think, and the trails were brand new so they were super slow. Like riding in 3 inch deep mulch.
There are some good trails on Mt. Van Hovenberg (sp?), and there is the jackrabbit trail that connects to a few others...but I don't really know them at all.
Apparently the appalachia conservation org (not the official name...I don't know what it's called) is paranoid about building trails and destroying the natural beauty of the area. If trail building could get started in a sustainable, smart way, LP could become super epic, like parts of vermont are today. you could ride forever up there...
for now, I'd reccomend taking your road bike. the iron man loop is pretty sweet, includeing about 9 miles of descending out of town, and 11 miles of climbing from the base of white face back up to LP. Mirror lake is great for swimming and chilling on the beach after long rides...