If you want to look for parking, check out
http://nyc.bestparking.com or
http://iconparkingsystems.com/for discounted rates. Are you bringing a regular sized vehicle with you? If you have a van, or an SUV, look for an open lot as many garages either have limited spaces for vehicles of that size, and if they do have spaces, charge significantly more. You can get weekend special rates in areas that are close to the Lincoln and Holland Tunnels on the west side, from which you can walk, take the bus, subway, etc. to places that you want to go. The train can also be convenient to Penn Station, but with several people, the cost could exceed driving. If you do drive, plan to arrive earlier in the day on a weekend, as that will help avoid traffic delays at the tunnels.
Initially, you may want to plan a trip to take the Grey Line bus, where you can hop on and off. In the Spring, you may want to take a Circle Line Cruise. You can also easily get to the Statue of Liberty and Ellis Island from Liberty State Park in NJ, and also don't miss the science center for your kids. You should also visit the Museum of Natural History and the Planetarium, as well as a multitude of museums.