Yeah, you might want to reserve those tickets ASAP as there's a massive waiting list for them. To answer your question, you definitely should go check out The Cloisters as Washington Heights is incredibly overlooked by many tourists. In fact, most tourists don't go beyond Harlem since they don't think there's nothing else to see beyond 125th street.
I suppose you could check out Nintendo World, even though it isn't really all that special and while you're at it, take a tour at the nearby NBC Studios (which I've never done personally and I've lived here my entire life).
While I've never been there before, you should also check out The High Line and maybe the Brooklyn Bridge since many people tourists love to take pictures from it. Of course, there's plenty more to see beyond Manhattan such as The Museum of the Moving Image in Queens but if you just want to see Manhattan for the time you'll be here, it should be fine.
The temperature will be relatively chilly around that month at around 45-50 degrees or so. I suppose the Morris Jumel Mansion might also be worth your interest as well (again, even though I live in the neighborhood, I've never been there myself, but I've heard good things about it). I suppose that's all I could really recommend unless you're interested in checking out China Town which is a tourist trap, but full of many shops in nooks and crannies.
I don't really recommend the Cloisters. It's nice and all but its basically on the opposite end of where everything else is and just not worth the excruciating trip back and forth.
There are also far better museums you could visit.