Why does that post remind me of the Simpsons episode when Homer buys a rifle "2 week waiting period? But I wanna shoot stuff now!"
I don't know how NY is, but around here (the Boston MA area) I can't think of any ranges that have rental access to guns. All the ranges I looked into were for members and their guests only.
If you really want to get into target shooting, I say go for the license, it might take a little more time, but then you'll be able to go to a closer range, and get your own gun, which will end up saving you money in the long run.