I agree that you should drive in, but should NOT try to pick up the relatives at JFK by car if you've never driven in NYC before.
A few tips:
- If you're in a rental car, unless they give you a toll pass that you decide to use for the whole trip (and pay the associated service charges), you want to avoid the Henry Hudson Bridge. That bridge only has cashless tolls and you will get nailed with service charges by your rental car company if you go over it even if you pay cash for all other tolls. All other crossings into Manhattan are either toll-free or have cash lanes.
- Street parking is generally pretty safe, but hard to find in Chelsea outside of weekends and you absolutely must read the signs carefully because tickets are very expensive if you mess up (or you can get towed). If you don't (or don't want to) find street parking, use http://nyc.bestparking.com to find good garage rates. The cost can vary widely between garages so it's good to research in advance.
- Most (but not all) garages WILL charge you the extra "oversize vehicle" charge if you are in a minivan, so be sure to compare those charges when looking at rates on BestParking.