I live in nyc, too. Range time is hard to come by so I set up a mini driving range in my living room. I hit against a futon, which is covered from the seat and below with a thick blanket (so thin shots don't get out of control if I miss under the futon). It's covered from above and to the right with added pillows (my misses are shanks to the right), and behind that is one of those egg-crate mattress cushions I picked up at Target to absorb misses that go high and right. I'd actually recommend hanging up 2x egg-crate mattress cushions because one doesn't quite absorb full shots.
I hit full swing shots off a golf mat, from PW-5 iron. Anything with more loft than PW is going to sky the ball into the ceiling and less loft than 5-iron hits the metal frame of my futon. I also use two full-length mirrors, one front-view and one down-the-line view to analyze my swing.
This range has helped me tremendously. I started just hitting chips and pitches, and after hitting 300 balls a day they became automatic. If you aim at a specific spot and use the same length backswing it becomes your go-to short-game shot. You have to go to an actual range, though, in order to check your distances, but once you know it, you can shorten/longer your backswing or change clubs to alter your distances.
With full swing shots, it helps ingrain your swing (whether with good or bad fundamentals obviously). That's why I use the mirrors to check myself and I pay attention to quality of contact and even how the ball bounces off the futon. A slice and a hook may hit the futon at the same spot (b/c it wouldn't go on its doomed trajectory until many yards past your futon), but you can tell by the way your ball bounces off the futon. If you sliced it, the ball will bounce to the left b/c of the side spin. If you hooked it, it'll bounce to the right. This is, of course, assuming your futon has somewhat of a flat surface. If it bounces straight back, it's usually a straight shot.
You can set this up without a lot of space. You just need a ceiling high enough. My apt is less than 500 sqft and I literally can't swing a club longer than hybrid without hitting something. But just to warn you, as you figure out where your misses really go, you may end up with a few holes/dents in the wall (which a little spackle can patch up easily). The best thing about it is that it's open 24/7!