The only bad part about New York is actually getting in here. You've got a few options to evaluate, but what's right for you depends on how many people are with you, your tolerance around city driving, and the tightness of your schedule.
You can always drive into the City. I've found that weekday traffic is pretty bad no matter what time you're coming in, even once the streets are clear of commuters weekdays are when there's more construction. I'd highly recommend using Google's navigation app if you want to drive into the city since it seems pretty up-to-date with traffic conditions that will route you a little better - especially since weekend events will frequently close a street or even an entire bridge/tunnel. But don't expect perfection, Google's Navigation is often more useful in rerouting you when you discover that a particular path is blocked.
Weekend all-day parking runs about $52 in the Upper West Side, weekday parking is closer to $21 if you're willing to brave the morning rush hour traffic to get there from 6-10am or need less than three hours. Note that Google Offers frequently has offers for Icon Parking for $23 the entire day. Icon is, well, an icon. They're all over the place up here (including one at my address) you'll just need to look for their logo (or find one online before your trip).
Street parking is also an option if you're willing to hunt. Below 96th is $3.50/hour with a two hour limit, above 96th is $1.50/hour. Look for a box next to the road and buy a ticket. Place this ticket on the driver's side dash and you're good to go. Note that Sundays and after 7pm street parking is free, so keep that in mind as well. Check out areas where there aren't many residential buildings, like in front of schools.
You'll also need to account for tolls. Coming from NJ you'll need to pay coming in, but egress is free. You've got the following options:
- George Washington Bridge: Gets you into Manhattan at the northern-most tip, but it's an easy ride down the highway-like Henry Hudson Parkway to get to the Upper West Side. You can get off on 79th to hunt for parking.
- Lincoln Tunnel: Probably a bit easier to get to from relevant parts of NJ, but gets you in around 40th so you'll probably end up taking surface streets north. 10th Avenue is probably a good bet (barring traffic) since it turns into Amsterdam. The problem is midtown traffic, it can be a bear and there are often closed lanes or streets.
- Holland Tunnel: Really just a good way to get downtown, I wouldn't recommend it for an Upper West Side visit.
The tolls are variable depending on how you're paying and when you're arriving. Cash is probably going to run you $13. EZ-Pass will save you a bit, $10.25 peak and $8.25 off-peak. There are plans for frequent travelers that can also help, but they're designed around commuters and may have a monthly fee associated with them.
Total cost to get into the city for most casual visitors will be $50 on the weekends for as many people as you can squeeze into a car.
Mass Transit - Trains
NJTransit will get you into Penn Station which is on 34th - 25 blocks south of the Park. From there walking is an option if you want to sight-see or explore, but the subway may be a better option. The 1 (red), B (orange) or the C (blue) will all get you where you need to go. Look for the Natural History Museum stop on the B/C or 79th street on the 1. If you miss these, all three lines hit 86th next which is also a good stop.
Cost here is variable depending on location. The subway is about $2.50 per person, unless you're under 44" and can pass for a kid. Note that MetroCards are prepaid, it costs you $1 to buy the refillable card but you only need one to swipe through everyone. The train from the Mount Tabor station costs $14 each way for adults and $6.25 for kids. From Hackettstown or Gladstone/Peapack it's 2 hours and $14.75/6.75.
Total cost for one adult makes this a great choice if the timing is OK for you - for less than $35 you're there.
Two adults and two kids will run about $85 depending on whether your kids are under 44" which makes driving a bit cheaper.
Two adults and four kids is closer to $100.
You can also drive to someplace a little cheaper, like the Newport Center Mall. Here covered self-parking is more reasonable at $10 for six hours or $22 for the entire day. A brief jaunt through the mall gets you to the PATH station where (on weekends) you can ride to Hoboken and then 33rd Street for the price of a subway ticket. You can then go from 33rd to the B line without seeing sunlight meaning that for $5/person and $10 or $22 additional per car you can get into the city and an extra $5/person gets you out. But it does cost you about 45-60 minutes from Newport to the Natural History Museum.
One adult would cost $20 for up to six hours, not bad at all.
Two adults plus kids would run $30.
You've got two options with the subway. The preferred route is to look for the numbers in the red circles and get on the 1 train Uptown or to the Bronx. You'll want to get off at 79th and head North or 86th and head South. Most of the time the exits are labeled with their direction. The northeast exit out of the 79th Street station will take you towards 80th St. on the east side of Broadway, for example. Note that the east exits are frequently northbound only and the west exits are southbound.
You can also look for the blue or orange subway lines and take the B or C to 81st (Museum of Natural History) or 86th. The benefit here is that you get to the Park faster, but really it's only a few blocks...
The downside of Penn Station is getting around in it. Jason Gibbs has an excellent set of maps that we can use to help out. Let's say you're coming from NJ Transit. The first thing you'll want to do is follow the signs to the Long Island Railroad (LIRR) to get to the lower level. From here you can go either right to the 1 train (look for the red circles with a 1-2-3) or the C (blue) trains on the left.
If you end up on an express train hope is not lost. On the 2 or 3 you can get off at 72nd street and walk the rest of the way or hop on a 1 for another stop. On the A or E trains it's not quite as easy. The E you'll need to catch early, but on 42nd (Times Square) or 50th streets you can still hop over to the C. If you get beyond that you'll probably want to call an adult. At 42nd (Times Square) or 59th (Columbus Circle) you can do the same to go from the A to the C, but if you miss that you'll need to backtrack at 125th street.
Meeting up elsewhere also works. Coney Island is an example of a good place to meet, you can get there by driving through Staten Island rather than Manhattan and we can try to fanagle free parking at the New York Aquarium (I get free parking and can leave with you, but if they need me to be there when you enter the lot that may be more problematic). Coney Island has the aquarium, but is also just a nice boardwalk with a sandy beach. And, of course, Nathans and the Cyclone.
The Bronx Zoo is another good spot. But being in the Bronx there isn't much else to do. Same parking rules apply, I get free parking but I'm not sure how exactly it works. Plus you'll still need to cross the GWB.
There's also the Staten Island Ferry as a poor-man's Circle Line. Meeting there lets us get a free boat tour past the Statue of Liberty and to the Financial District.