So I've been in NYC for six years and tend to have to do touristing things with visiting family and friends so although I haven't read every post (I've read quite a few) I'm going to give you my advice and opinions.
1. Most museums in NYC are suggested admissions but know that if there is a special exhibit if you don't pay the full suggestion you may not get in. Typically the MET and Natural History will have 2 or 3 big exhibits outside of their always there things and those extra exhibits require you to pay the full price of the suggested admission. Also some exhibits or experience may cost even more. I love the Met and Natural History Museum but hate the MOMA. The MOMA (museum of modern art) is always crowded and even though I love art I'm just not a fan of modern art. Interestingly enough it isn't like I'm uneducated or anything like that as I did study art and art history I just don't care for modern art.
I think we will try to see the MET and Natural History. I checked the TOTR and MET combo pack. I have added it to my list. Added later: I think this is TOTR and MOMA combo pack!
2. The NY pass is really only worth it if you want to go to all those places. Also remember anything that is offered on the pass will probably be busier than things not on it because a lot of people get the pass.
I don't want to run around the city to get our money's worth ($600) with the NY pass. I have checked the Explorer pass (for 3 attractions) from Costco from a previous post. We might get that instead. I have to talk to DH first.
3. In my opinion the 7 day metro card is always worth it for people on vacation. The only problem is you are in a relatively inconvenient area of midtown. Lexington is pretty Far East (I live on 29th and lex) and so your train options to get across town will almost always include a transfer. The shuttle (S line) between Grand Central and Times Square will become your best friend. Just remember the S doesn't always run (it is off between midnight an 5 am) an if you are stuck taking the 7 it is typically easier to just walk across town.
I didn't realize our hotel was so far from other things. How many miles is from 37th Lexington to Times Square? Can we walk that distance?
Now for advice on you physical trip. Anything you can get on TKTS will be a show that already has discounts up. So if Spider-Man is on TKTS consistently they probably have a special where you can pre-buy your tickets for pretty close or cheaper than TKTS. Also you are going during the busiest week for the city so little to nothing will be on TKTS. Also the lines will be 3+ hours. Please don't waste that much time on getting broadway tickets especially on your vacation. Broadwaybox.com has almost all the currently offered Broadway discounts and you can prebuy online. Anything that is new or amazing is probably already sold out or won't be on TKTS. Just a sample of what is on Broadwaybox is Spiderman, Newsies, Annie, Chicago, Jersey Boys, Rock of Ages, and Phantom. I do stress only use broadway box for the discount codes. If it doesn't say discount then sometimes the tickets are from brokers. They do give a warning though if you aren't buying them directly from the show itself so that is alway good.
For your family and ages I would suggest Newsies, Matilda, or even Annie. I saw Spider-Man and although I thought it was ok there is so much better theater out there. Just as a heads up the Newsies at CA is nothing like the Newsies on Broadway. I don't even think the Red Car Newsies sing any of the real Newsies music. Matilda is amazing and fun. Annie is just a family friendly classic.
I will definitely check Broadwaybox for tickets before we go. I just have to decide which show to see, DD12 is at an all week overnight Air Force Academy sports camp. She will be returning home tomorrow. I will ask DH and DDs this weekend and decide to buy the tickets.
Now I saw you wanted to see the fireworks from a rooftop for free. Just a heads up the free 4th events are usually packed. Your whole hotel will probably have the same idea. Also as I already pointed out your hotel is very Far East where as the fireworks are all the way West. Many of the fireworks and water level. When they first moved the fireworks to the Hudson I only lived 4 blocks away from them and you couldn't see much from our rooftop. This is just a heads up on the situation.
I just realized that we will be in NYC with all those tall buildings
. We will probably not see the fireworks from the rooftop. Our town has a huge 4th of July party with fireworks every year, If we don't get to see fireworks this year, it's fine too.
Oh I've done Ripleys and it is simply not worth it. None of it is the real stuff it is just all models of the real Ripleys collection. I felt do taken advantage of when I went.
I just asked DD15 about Ripleys and she said it is ok if we don't get to do it. I removed it from our list for now. I prefer doing NYC stuff.
This post is getting really long but I feel like I could tell you so much more so if you want more advice or specific things I can give you more.