Hi Wanderer!
I love NYC too; we just had another trip there in early June for a wedding + sightseeing fun of some things one or both of us hadn't yet done and re-visits of some we had. Recommended hotels may depend on what sorts of amenities you prefer, and how many of you will be traveling; as you use "I" a lot in your first post, it's just you or will there be more?
We like having specific amenities enough to base our choices on those + reviews, location, + room configuration. Expect smaller rooms than you may be used to but some do a much better job making efficient use of the space so they don't feel as cramped. I also back away anymore from anything charging resort fees for amenities we don't use. I might also expect an up-front, per-night damage fee that will be refunded after your stay but this is becoming more and more common amongst hotels all over the country. Do you have specific preferences?
Given your sightseeing list, you will be using public transit or paying for cabs/ubers as Ellis, the 9-ll Memorial, Wall Street & Battery Park are way down on the southern end, and the Met, Frick, Central Park and Neue are much further north. You could pick a location in between or just find something you like on either end and just deal with longer commute times. Personally, I'd choose something around Midtown, and especially so if your "etc" includes MoMA, a look at Grand Central Terminal, Rockefeller Plaza, JP Morgan Library (just did this one and can recommend) and some architectural stuff in the area.
How many days? There is SO much to see, and I've no idea if you're a "take your time" museum browser or move at a pretty good clip. Also what you have on that "etc" list; some of us can recommend even more based on your interests. The Met has been a lion's share of a day for us, as was the 9-11 Museum (do the museum; not just the outdoor memorial!!!!). MoMA didn't eat quite as much as we moved more rapidly through sections not of huge interest. You could probably do the Frick and Neue on the same day.
So give a shout back with more about your trip? Happy to forward name of Midtown hotel we used most recently if it sounds, from that additional info, if it might work.