I travelled to New York by car from another state. No one warned me not to park on the street. My car was broken into twice (two nights running) before someone told me that I should have parked it in one of the secure car parks. Better advice would probably be not to drive, however if you do need to take a car into New York, I recommend using one of the many lock-up garages.
many locations across the city
Theft and vandalism aren't that big of a problem but it's not like they don't happen. On the flip side, if you drive it anywhere worth going, you'll have to find parking on the street which by itself will take longer than getting there by subway. If you park in a lot or garage near each destination, it will cost you dearly. It's not worth it. In general, a car is only a good idea when you want to visit places outside the City, IMHO.
One other thing, if you drive here from elsewhere, leave it in long term parking at an airport and use subways, buses and cabs. A car is also fun but see the City like a NYer who generally only have cars if they live in an outer borough where parking on the street is much easier. It's too expensive in Manhattan to always pay for a garage or lot.