You don't tend to think of New York City as being a great place to own a car. The area tends to be very packed. In Manhattan, for instance, you will likely have to either jockey for parking spots with tons of other people and switch spots to avoid the alternative side rules, or you will have to park in a garage. The garages charge quite a bit of money, which many people just can't afford (when you combine it with what they pay for rent for a Manhattan apartment). However, there are neighborhoods in the city that are not as congested and where you can find a house with a driveway. These neighborhoods will be located in the outer boroughs (you won't find this in Manhattan). Here are two nice neighborhoods to look at where you will find homes with driveways.
Bay Terrace, Staten Island
Staten Island is a borough that is well suited for car owners. The borough is much less developed than Brooklyn, Queens, or The Bronx. The number one complaint that most people have is that the public transit on and off the island is difficult (a ferry or buses--no subway). However, it's a really nice place to live if you do have a car. You can drive into Manhattan via the Verananzo bridge (into Brooklyn and then into Manhattan). Plus, you can find a big house with a driveway. There are even homes with backyard pools. Right in the city!
Bay Terrace is one of the nicer areas of Staten Island. It's located near the shore, so you are really close to the water. That's great if you are the type who likes to go fishing, boating, or simply jog along the seashore.
Throggs Neck, The Bronx
The Bronx has a few neighborhoods that are predominately houses. One of them is Throggs Neck. It's in the southeastern section of The Bronx. It is located right next to the Long Island Sound. It's made up mostly of single family homes, and has a very quiet vibe. It's much less industrial or commercial than neighborhoods to the west. The more industrial, densely populated Soundview neighborhood is physically separated from Throggs Neck by both the Hutchinson River Parkway, and the Westchester Creek. So, Throggs Neck is rather isolated and quiet. This makes it perfect for families looking for a place to raise kids. The area doesn't have great subway service, but it is very convenient to get onto the Cross-Bronx expressway, and then take that to the Major Deegan and drive right down into Manhattan.
For more help finding the right home where you can keep your car, contact a professional real estate agent, such as those with the Dave Kaercher Team - RE/MAX Real Estate Group.