Most of the things you'll want to see in downtown are within walking distance of most of the major hotels. Driving around downtown can be a hassle, but seeing as you're from NYC, I'd imagine our traffic problems will seem minor on comparison to what you may be used to.
There are several tour companies in Vancouver that offer some very good tours of Vancouver, Whistler and Vistoria if that's what you're interested in. I'd recommend Gray Line of Vancouver, simply from personal experience. I've been on a few of their tours with out-of-town friends and they are great tours. Vancouver Trolley Company offers a loop tour or Vancouver where you can get on and off at any of the 20 or so stops they have. Gray Line also offers a similar tour on double-decker busses. There's a horse-drawn trolley in Stanley Park that will take your around the whole park in about an hour. There's a guy with a very cool vintage car who gives personalized tours of Vancouver from the Pan Pacific Hotel. Can't remember his name, but its a neat car from the 30's I think and seems like it'd be kinda fun. If you're staying at one of the major hotels, the Concierge, Doorman or Front Desk should be able to set you up with whatever tour you'd like, or at least put you in contact with the appropriate company. So if all you want is to see the sights of Vancouver, you probably don't need a car. On the other hand, it might be an idea to take one or two tours, then get a car and go back to the places you'd like to explore more on your own time.
As far as hobby related things, unless you're wanting to tour the street-walker Tracks, a car probably isn't necesary as most of the ladies in town (either independants or through agencies) will gladly visit you at your hotel. Besides, it'd be damned inconvenient to get pulled over by the local boys on one of the tracks, and rentals cars scream "STOP ME!!"
If you're wanting to go see some dancers, the best bars (No. 5 Orange St., The Cecil, The Marble Arch) are 5 - 10 minutes away (generally) by cab.
Hope this helps. Enjoy your visit.
SWG