First off in NYC you can not have one in the city. Their are a couple of gun stores outside the city that offer the option of storing the rifle for you (most want you to buy from them for this option to be in effect). For a low priced rifle you can look at used DPMS, STAG or EAGLE units. Check out gunbroker, auctionarms, or guns america for any deals. Sometime you can get a steal on one for around $500, but you are most likely gonna pay around $700 for one that has a couple hundred rounds down the barrel.
If you want to biuld one then you can piece one together for around 500 on the cheap or around 700 with quality parts. Plus building one lets you really "know" the gun. I have posted complete instructions here in the past (see my previous threads or just search here). Also AR15.com has an excellent guide with photos that I linked to as well in the past. Other than a few special (and essential) tools you can put one together by yourself.
Lifetime member VFW and NRA
"Quando Omni Flunkus Moritati" (when all else fails play dead) -Red Green