I have NJ permit is that honored here if I want to rent a handgun and can I shoot larger than .22?

No, unfortunately NY does not honor any other state pistol permit. Westside only has .22 cal rifles to rent and fire. If your interested in firing pistols or assault type rifles would encourage you to look into Penn, which allows it. Do a quick Google search for a range nearest your home, call ahead, inquire as to rates, rules, reserve a spot. It is important to call ahead, some ranges have meets, tournaments, and could be booked for a specific day. Penn is where I go with friends without a NY permit that want to try out the sport. Enjoy!

Thank you, just thought I'd try in NY after work.