Thanks for all of your responses. So, here are more of the specifics...they've been coming together over last few days...and we have a bit more time.
Thursday, June 26th - two adults and two kids (ages 11 and 8) arrive late afternoon. May take train into NYC for a night out. May just hang at hotel. Depends on how smooth the flight goes. Planning to stay at the Hilton Penn Station near Newark (near the port...taking a cruise).
Friday, June 27th morning - plan to take the train into the city. Plan to see Central Park, a museum by the park or the zoo, and FAO Schwartz. We can move at a pretty good clip, even with the kids who are used to traveling. This day will be mostly about the kids.
Friday, June 27th afternoon - grandparents fly in. Grandma had a hip replacement, but working to get up to a mile of walking at a time. She has some trouble standing for long periods too. Stairs are out for her. We will have to reevaluate any itinerary closer to the trip, but plan to either hop on cabs or walk slowly, or both. We should have time for something this evening, assuming a 5pm start. Staying at Hilton Penn Station again.
Saturday, June 28th morning - we board the cruise this day. Boarding starts at 11am (I think). Have to be on board by 2pm. Could have some time this morning.
Thursday, July 3rd - arrive at Port Liberty at 8am. Planning to stay in/near Times Square, possibly at Hilton. Need to assume a noon start to any sightseeing. Want to see a Broadway show this evening, maybe Wicked.
Friday, July 4th - we have all day. We are staying overnight (again possibly at the Hilton). We are okay with walking to the fireworks. I've given up on a room with a view of the fireworks, given that we definitely want to be near Times Square.
Saturday, July 5th - we are headed to Cooperstown early that morning. Grandparents fly home.
Friday, July 11th - we are headed back to NYC for the night. We need a place to stay (one room, two double beds) for this one night. No grandparents, since they flew home already.
Saturday, July 12th - fly out of LaGaurdia late afternoon.
Hope this isn't too much detail.
For rooms, we just need one for our family, since the kids can still sleep together on a double bed, and one for the grandparents.
Must sees for the whole group include: Statue of Liberty (maybe the pedestal for grandparents and crown for the rest), Empire State Bldg, 9/11 Memorial, Broadway show. For the kids, Central Park, FAO Schwartz and Toys R Us Times Square. Other ideas: South Street seaport, American Museum of Natural History, Metropolitan Museum of Art, MOMA, Top of the Rock, High Line. I would only take the kids to one museum (if any). Would consider taking grandparents to Central Park, if there was something for the grandparents to see w/out a lot of walking. They've never been there.