There's usually no reason to get a pre-arranged car service from JFK. A taxi s generally the same price or cheaper (unlike at EWR). But never under any circumstances take a red from one f the hawkers at the airport.

Speaking of those hawkers at the airports offering rides into the city - don't understand why airport authorities don't put a stop to this - it is blatantly illegal and these guys are known to be rip off artists.

Sorry about my typing last night. Let me make a quick correction. The cars hawked at JFK aren't necessarily "red". But they are always illegal and not a good ideal.

And I'll make one more addition to my suggestion. If you are arriving at JFK at a very busy time (a holiday or a really snowy night) then it might be a good idea to reserve a car service because taxis could be in short supply. But my experience has always been that taxi lines are normally pretty decent (no more than 10 minutes). But I got stuck in a 2-hour line at LGA right after our Christmas snow storm and ended up taking the airport bus. The hawkers there were trying to get people to pay $50 per PERSON for a ride into Manhattan; it's normally about $40 for the full carload.

Thanks for all the information, it is great! To burden people even more, could you recommend any plays. We have used TKTS in the past and were happy with the results. I read one article critical and another praising "How to succeed...".
Nothing too risque or depressing would be fine. Off-Broadway is O.K. as long as it is not too far away.

Re shows -
There's a thread on here called "Broadway Banter" that discusses the shows on Broadway. It's a great resource to read Fodorites' opinions.

This link may be helpful to see which shows MAY show up at the TKTS booth -
http://www.tdf.org/TDF_SupportPage.aspx?id=68&do=v

Here's a great site for Broadway discounts -
http://www.broadwaybox.com/
Look at the list on the left for shows that have discount offers.
Sign up for their email and/or on Facebook to get regular updates re discounts.

Most of the time I prefer buying a discounted ticket online ahead of time rather than "wasting" NYC time waiting in line at the TKTS booth. If the "savings" is only 10% of the original ticket price, I'd rather be out seeing the city than saving $5 or $10.

Well I hoped to recommend Spamalot, but it closed a couple of years ago!