First of all, they are not the only teams that don't play right in the city they represent. For example, the Redskins play in Landover, MD. Anyways, that was where they found space to put a stadium+parking, and its probably more beautiful/pleasing to the eye than the middle of NY.

cheaper plus is really close

B/C NY already have 2 baseball stadium

Because that's where the city could find affordable land to build the stadium.

where is there room in new york city?

Because Giants Stadium is located there. Where would you have them play? The Polo Grounds?

Because land in NYC is uber-expensive. And it's really close to NYC, so it all works out.