Drive into the city??? Uhmm, would not be my first choice. The trains are easy to use and work quite well. We have used them when staying in Jersey, adds time but not a bad choice. I don't remember the name of where we stayed since we were visiting friends in NJ it was based on proximity to them rather than the city anyway.
You can get some great deals near the airports if you are looking to stay cheaply. Of course, there are a plethora of hotels in NYC, but most (decent) ones are quite pricey. So convenience in this case really carries a hefty price tag. We have found that sometimes the convenience and price was worth it, sometimes not. It depends on what you are looking for. If you chose to stay in the city (I realize you wrote you are looking for outside the city) there are still some good places to stay. In Nov. we ended up a rather dull but nice and clean Marriott in the financial district (near the statue of Lib ferries and ground zero, not so close to times square) for a 4 person room and breakfast for about 360 per night, which for NYC was reasonable.
We have also tried to stay at
Bubba and Bean's but there has never been any room when we have wanted to go. So although I have never stayed there, we have heard good things about it.
May not be what you are looking for... but maybe a place to start.