Hopefully, I can catch you before you go. First, welcome, and have a great time.
Secondly, as a cop, and a New Yawka, don't be a typical tourist.

You'd be shocked at how many people can't manage a simple grid system to find their way around. Here's your navigation guide for most of Manhattan. There are four cardinal direction, Uptown, Downtown, Eastside, Westside. Avenues run up and down, streets east to west. Streets east of fifth avenue are prefixed East, and west of fifth avenue, you guessed it, West, and the building numbers progress from that axis. Thus, "2 East 86" would be right off 5 Avenue, and "200 East 86" several blocks further east. Avenue building numbers begin downtown, and ascend as they proceed uptown, with (usually) odd numbers on one side, and evens on the other. On streets, odd building numbers are on the uptown side, and evens on the downtown side (so, you'll always know which way is up or down by checking the numbers). As a GENERAL rule, even numbered streets run east, and odd ones west ("E=Even=East"). Pretty simple.
Please don't stop in the middle of a sidewalk; step to the side if you have to fiddle with your phone, or if you're walking much slower than everyone else. Read a local newspaper each day (I prefer the Daily News), if for nothing else, but to check the traffic reports; knowing where traffic is backed up, some dignitary is shutting down streets, or where protests are headed can make getting around a lot easier.
Places to go: The Met has been mentioned, but The Frick, and the Neue Gallerie are splendid, as well. A Rangers game at the Garden could be fun. Signing up for "Club Free Time" gives a lot of options.
Eats: Sevilla, on W 4th and Charles in the village, is my favorite restaurant, and I've been going there for almost 40 years. Outstanding Spanish food, and a great neighborhood for walking off a full belly. Wo Hop is good for some sloppy Chinese. Katz's Delicatessen is a MUST; the pastrami is SO good.
Have a great time, and if you need anything, don't hesitate to PM.
