Depending on where you're coming from in the south, driving could take a full day or more (with an overnight hotel to pay for) each way, so its not the way I'd choose. Flying in would be the best use of your time.

Staying in Manhattan is more expensive but will also give you convenience and more time in NYC. Not all areas "out of town" have convenient public transportation into the city at all hours, and some would require you to spend $50 per day in back and forth costs plus the time you'd lose. Manhattan has many areas that are popular but aren't necessarily called "downtown" like they are in other cities. As long as you're near subway stops, most areas in Manhattan will be fine so you should see what's available in your price range and people will comment on them specifically

Your son wants to come to NYC--what does HE want to do or see? What are his interest? What are the "obvious" places and are you going to them or planning to skip them?

If your whole trip is based on NYC, fly, don't drive. Parking is very expensive and you would leave it in the garage the whole time. Do NOT stay outside of town;you'll waste time and money commuting back and forth and won't have a real NYC experience. The weather could be very warm, and it's nice to be able to return to your hotel room to refresh yourselves.If you have to drive, there is advice on this forum where you leave can leave your car outside of the city, NJ, CT.
Stay in Manhattan, many wonderful areas of the city to choose from.Most first time tourists stay mid-town but the excellent subway system makes it possible to get all over the whole city quickly and inexpensively.Personally I would prefer to be a little farther downtown. With 4-5 days, your time will be booked solid seeing the highlights.
Look at Fodor's NEW YORK, a free app for your iPad or phone.Or,click on "Destinations", on this website.

Well, you've already helped me decide to fly instead of driving. I checked a few package deals on Travelocity just very quickly, and was surprised at how affordable the prices actually were. My son wants to see Empire SB, Hudson River, Giants stadium, Central Park, Ellis Island, Wall Street, and Times Square (and a Broadway show). I'm pretty flexible, but would love to do a bit of shopping too.

First of all - in NYC downtown is NOT the center of the city which is what I assume you mean. Manhattan (the center of the city ) has a bunch of neighborhoods - including downtown (which is primarily the financial district/government center) but doesn;t have most of the tourist sights - which are midtown or uptown or on islands in the harbor.

You should definitely stay in Manhattan - to avoid wasting a lot of time and money commuting in from an hour or more away. The only hotel in Manhattan with free parking is the Travel Inn on the far west side. This is a reliable modest property. Any place else you stay you will have to pay for parking (either in the hotel or a public garage nearby - expect $30 to $35 per night for that.

If you give us a budget people canmake recos as to where to stay.

And if you tell us specific interests people can make recos on activities.

Basics for all are:

SoL and Ellis Island (get ferry tickets far in advance from the National Park Service to avoid very long lines)
Top of the Rock
Central Park (look at the web site of the central park conservancy_
Staten Island ferry (free ride across the harbor - 25/7)
Museum of Natural History
Intrepid Air and Space Museum with Space Shuttle
At least one B;way show (get discount tickets in advance from broadwaybox.com)

Sorry -

Before you buy any travel packages look very carefully at hotels. Many of the web sites list hotels in NJ or out at the airport as being in NY. You do;t want that - will be a huge waste of time and money. You want a hotel ONLY in Manhattan - and there are even some of those you don;t want.

Come here and sk about the hotels, check them on tripadvisor - and make sure you locate them on a map - and they re near a subway stop in Manhattan only - not Queens, Brooklyn or Bronx.

Have you bought yur guidebooks yet?

FYI: Giant's stadium is out in NJ. You'd need to take the train from Penn Station to Secaucus. Or if you land at EWR, you could see it on your way in to the city.
Glad you're flying!
If your son is a movie buff, TV too, include the Museum of the Moving Image. It's in Queens but an easy subway ride from Manhattan.