What are you into? Museums, restaurants, shopping? My main advice would be to stick to one neighborhood a day, or maybe even one neighborhood the entire trip (e..g, pick one from times square, downtown/financial district, SoHo, Museum mile). Common mistake is to try to traverse the entire island of Manhattan in one day which is just exhausting.
The West Village is a nice place to walk if you just want to explore a neighborhood. It’s a fun mix of historic charm, restaurants and shops, and arts and entertainment (indie theaters, comedy clubs, jazz clubs, etc.)
Those dumplings on Eldridge Street are insanely expensive. Vanessa’s charged something like $3 for 8 pork/chive dumplings, unreal! But damn they’re good. I spent a whopping $8 for a meal there, what a joke.
Take a subway ride to Williamsburg, Brooklyn. Some think it’s overplayed, but I disagree. It’s quaint in a way that prime Manhattan doesn’t really offer. For example, there’s a tiny restaurant called Juniper, I don’t know how it stays in business. It was one of the most pleasant evenings I’ve spent in a restaurant, a classic NYC experience. Plus it’s BYOB, which is kinda cool. Don’t go if you’re in a hurry, because you or they won’t be rushed.
If you’re into swing dancing or swing music, check out events by Prohibition Productions. There is also often live swing music at The Django. For more traditional jazz, The Blue Note, The Vanguard, and Dizzy’s. The late set at Dizzy’s is one of the best deals on live music in the city - $5 if I’m remembering correctly, and the venue is super nice.
Tanoshi Sushi seems like a hole in the wall but is one of the best omakase sushi deals in the city. Humble surroundings, great food.
The Metropolitan Museum of Art is a common destination for visitors, but New Yorkers love it too. I’ve been there multiple times and am in awe every time. It’s very much worth a visit if you haven’t been.