Unless you have an appreciation for art then I'd personally skip a lot of the art museums there. We went to the American Museum of Natural History and that was a lot of fun, and I imagine I had a much better experience there compared to staring at abstract art, but that's your call
The great thing about NYC is the overabundance of free things to do and see outdoors, that you could probably get away without having to fill your entire visit full of paid tourist attractions. Obviously, every person is different, so maybe you can post up what you're thinking of seeing/doing and we can give you a better idea if it's something that's worth it.
Bouley has since moved locations and is now located at 31 W 21st St, New York, NY 10010, USA (21st & 5th Ave - close to Flatiron Building & Madison Square Park & Shake Shack)
Bouley Lunch Tasting Menu · Bouley at Home
Their lunch tasting menu has gone up from $55 to $59 now, but it's still what I'd consider to be one of the best tasting menu experiences without having to necessarily break the bank.