I live in Dayton, I moved here about six months ago. Yes, there is about a 30-mile paved bike path that is really, really great. Well maintained, far nicer than riding on roads. I haven't navigated the entire trail myself, so I can't really clear up any confusion for you.... Im still confused on where it goes myself!
Yellow Springs is a beautiful area, I really love it and wished I lived there. Depending on where you're in school, its a bit of a hike but the area might be worth the commute. There are many trails and state parks right near there (Glen Helen preserve and John Bryan state park). There isn't a ton of mountain biking, but a few shorter trails. Beautiful hiking, though!
Let me know if you have any questions, it's not a bad area. Good luck with your moving plans!
Believe in what is possible.