i will be at the fire training academy for the next week starting tomorrow.night

any good guns shops  around

Nothing really to do in mountor falls. You are close to Ithaca and Corning though. Ithaca is the place to go and watch people. The commons is pretty entertaining. Corning has some good bars and Good eats. You are also close to Watkins Glen. Some nice views if you are into that.
As for gunshops, I have given up on them in NY.

If you make it to Ithaca, drive a few more miles to Dryden and drop in at Boltworks on Beam Hill Rd.

Watkins Glen State Park is maybe three miles away and a nice, relaxing walk. Plan on two hours. It's about two miles in (and the same back) and raises like 400' in elevation. Park at the bottom, on the street and walk into the park (Don't give "The Duce" anything towards his million $$$ plus parking area). Word... Don't climb the last few sets of steps at the upper end unless you need to use the facilities. Not much up there other than the upper parking lot, bathrooms and maybe a place to get a sandwich, if it's open. There shouldn't be too many people there right now because kids are back in school and it's a little too early for the leaf peepers.

Map: https://parks.ny.gov/parks/attachments/WatkinsGlenWatkinsGlen.pdf

After the first day, you'll be tired of the Academy food. Jerlando's is a family owned Italian restaurant in "Downtown" Watkins. Get yourself a Scuteri's Cannoli for desert, go around the corner from Jerlando's and head towards WalMart. It will be in the front of a house on the right side of the street.

Always remember, "A bad day at the Academy, is better than a good day at work"!