Carnegie Hall

I can't answer all of your questions, but hopefully some of this info will help. I sang at Carnegie Hall with my choir when I was a senior too, so I can promise you that you and your family are in for a treat!

You do not want your own car in NYC. Parking is hard to find and ridiculously expensive. Plus, many places are walkable or easily accessible by subway. You'll be SO much happier if you don't have your own car to deal with. A cab from the airport is, I think $40 flat fee to anywhere in Manhattan, plus tip. Or, if you fly to Newark, NJ airport, it's easy to take the train or bus to the city instead.

Statue of Liberty & Ellis Island are the same place and they are not too far from Ground Zero. Plan to do those at the same time, since they aren't too close to the other things you mentioned above.

For a Broadway show, you can get discounted tickets at the TKTS booth in Times Square. You can walk from Times Square to Broadway and to Carnegie Hall pretty easily. You can walk to the Empire State Building and Central Park from these places too. They're also near Radio City Music Hall. Midtown is not that spread out and you can easily walk around to see all of these different places. You can window shop at the fancy 5th Avenue stores too.

Jerry's Deli... do you mean the chain restaurant? NYC has several famous delis in the midtown area (and other parts of the city). Ask around for recommendations, since Jerry's probably isn't your best bet (but I'm blanking on the names of the others right now)

Expect to pay upwards of $200 per day for a hotel room and even more than that if you want a suite.

I know you don't want to have to look a lot of things up, but I do recommend getting some sort of guidebook with good maps inside, since it sounds like you really don't know the layout of the city. It'll save you a lot of time and prevent you from getting lost.

I have never been there, but my mom used to go there quite regularly on business. She never had her own car, and would go on her off time to visit all the attractions you mentioned, with the exception of going to a show taping. I believe a cab, the subway, and/or train would be able to take you anywhere you need to go. Maybe you will even win a bunch of money on Cash Cab!!! :)

How exciting -- you will have a wonderful time! I lived in Manhattan for 4 years and I agree with all the other posters that you do not need or want a car in the city. If you drive to the city instead of flying, plan to park your car at the hotel and don't take it out until you go home. A good guide book like Frommers or Fodor's can tell you what it will cost to park your car at the hotel for the duration of your trip -- it may be significant enough that you would rather just fly! Once in the city, you will find it much easier to take the subway or cabs. Cabs are expensive, and you won't be able to put more than 3 or possibly 4 people in one, so given the size of your group I expect that you will ride the subway a lot. The subway in NYC is great -- it can take you anywhere you will want to go. The city is huge though -- the guide books will have good itinerary suggestions and walking tour suggestions for how to group the sites according to location. Basically, though, its common sense. The lower part of the island has Ground Zero, the Statue of Liberty and Ellis Island, the financial district, China town and Little Italy. Moving North, you have Greenwich Village and Soho, Midtown, Central Park, and the major museums. If you want to see a broadway show, but are flexible about what show it is, then TKTS is the way to go. They sell the unsold tickets in the middle of Times Square the day of the performance for a good discount. They might not be the best seats or the newest shows, but its worth it! Stay in Manhattan, not an outer borough or the 'burbs. The commute into the city each day would be a drag. If Southwest flies into one of the NYC airports, I would suggest doing that. There are lots of busses and van services that will take you from an airport to a central location in NYC like Grand Central Station or the Empire State Bldg. This is a good way to go because the price is much better than a cab but you get the convenience of cab-like service out of the airport. There is no really good public transportation into the airports, but once you are in the city the subway is great. Good luck!

My daughter's dance group went to NYC a few years ago. We booked an apartment for the week and split the cost. It was MUCH cheaper. I found it on Hotels.com or something like that... I can't remember how I found it but I think I googled executive suites or something... YMMV...
We traveled by foot and subway with no problem at all.
I would recommend going to your library and getting all the NYC travel books you can find. I also recommend a little map book that costs $5 or $6 that unfolds into a map of the city. I think I found mine at Borders...
Have a great trip!
LBC