Might I suggest the Intrepid Sea, Air and Space Museum?
https://intrepidmuseum.org/
You can tour inside an actual aircraft carrier and submarine.
And the Radio City Stage Door tour
https://www.rockettes.com/christmas/experiences/tour/
It's a fabulous, fully restored Art Deco theater from the 1930's. You get to see all of the backstage workings, costume rooms, and memorabilia, and you get to chat with a genuine Rockette. The location is midtown, by Rockefeller Center, and just south of Central Park, which is a lovely area with excellent shopping.
Finally, a plug for one of my favorite restaurants, also in midtown just by Union Square Park. It's lovely, and the food and service are fabulous. Book ahead on the website, as it tends to be booked weeks or months in advance. Lunch is a bit cheaper than dinner and just as good.
https://www.unionsquarecafe.com./
Finally, as a former bartender, please follow the local custom on tipping, even if it makes no sense to you. Servers in the US have to "tip out" to the non-tipped workers (bussers, food runners, kitchen staff, etc.) as a percentage of their sales and can lose money on your table if you don't tip appropriately.
We love our British tourists, and I'm sure you'll have a wonderful time. Don't hesitate to ask if you have any questions you think I might be able to help with.