https://www.trailforks.com/region/corni ... =-77.14529
There's an app too and it works offline if you cache the area so you can take a map "with you" when you ride.
Looks like Erwin Wildlife Management Area has trails. Really close to you. Looks like you have a bunch of options in a 1 hr drive.
As far as the bike, I'm not sure. You could try calling local shops and see if they have a rental or "demo" program. Expect to pay about $100 a day to "demo" a bike. A "rental" is probably cheaper like $50-70 a day and maybe a weekly rate that is less. But a decent way to see if you want to get into it or not. "Rental" = meh bike, "Demo" is usually the big dick $6k+ bike.
Babcocks Bike Shop in Endicott would be worth a call.
Wheels Unlimited in Bath
There are a few in Elmira that may work
Or maybe Chenango Point Cycles in Binghamton
Check craigslist if you want to buy a bike to try it out. But there's not much in Corning itself. Would be worth a drive to get something.
https://ithaca.craigslist.org/bik/d/bro ... 86858.html
https://elmira.craigslist.org/bik/d/201 ... 58119.html
https://rochester.craigslist.org/bik/d/ ... 06531.html
https://rochester.craigslist.org/bik/d/ ... 57242.html
New bikes are going to be a lot more.
Please please do not ride MTB without a helmet. You hit your head way more on the mountain bike than you do cruising around a neighborhood.