New Yorker here. the time at museum is great, also check out Eldridge Street synagogue Museum when you’re in the neighborhood. It is incredibly restored and the history is fascinating. Check out when they have guided tours (free) because it adds a lot of the experience. You can get great cheap eats at many places in Chinatown, as well as lots of lower east side favorites. You might be interested in a walking tour, big onion does good ones in various neighborhoods.
For a combination, history, nature spa day, take the ferry early to Governors Island, and visit the q.v. spa there. It has amazing views, lots of different steam, rooms, and saunas and pools, and is a lot of fun. For a simpler spa day, you might enjoy the Aire ancient baths in Noho.
I walk all over, including across the bridges between Manhattan and Brooklyn, where I live. I also love biking, especially in central Park. You can rent a city bike and bike all over, including getting to places where there are very few people and just beautiful scenery.
The Whitney Biennial is on now. It’s not my favorite but it’s interesting and combined with a walk on the highline and visit to Chelsea market would make for a fun day.
I also highly recommend coming to Brooklyn and checking out the Bk museum, time out market, the views from the promenade etc.