Sent my mate this the other day based upon my experiences/where I'd visit. You've already mentioned a few on here, I'd definitely go to Jean Georges. Per Se would be amazing but getting a booking is very difficult and you're talking $400/head. Give WD-50 a go too:
Formal places:
Jean Georges - Probably the best value 3 michelin star restaurant in the world. You can eat lunch there for $28/head. It's quite a smart/formal place but one of the top places in the US and would be number 1 on my list (i missed out on going there last time)
Daniel - Formal, french food, but is consistently rated as one of the top restaurants in NYC, not cheap though
Le Bernardin - Formal, supposed to be superb seafood. Like Daniel not as cheap as Jean Georges
Interesting/other places:
Perry Street - Run by the same people as Jean Georges, they also do a really, really good value lunch but it's less formal.
WD-50 - Casual restaurant, it's a really relaxed, friendly atmosphere but the food is really interesting with some unusual combinations, similar to Sat Bains/Heston Blumenthal in style
Peter Luger - There's loads of top steakhouses in NYC, but this one is the one everyone goes for. Very traditional but they get all the best beef in NYC
Momofuku Ssam Bar - Supposed to be a really good Korean/American place which shouldn't break the bank. Doesn't take reservations, you have to turn up and hope.
Sushi Yasuda - One of the best Sushi places in NYC but not as expensive as most
Worth mentioning but very expensive:
Per-Se - Supposed to be one of the best restaurants in the world. Very difficult to get into and /very/ expensive but supposedly worth it...
Masa - Well I guess it's worth mentioning. Per Se is expensive, but this place makes it look cheap. I believe it's about the most expensive place in the world at ~$400/head. You basically get served whatever the chef feels like serving you as part of a tasting menu style.
Also try the
burger bar at le parker meridien at some point - I ended up going twice! It's a really cool place. Oh and if there's one place I'd say to avoid - Bouley. Went there and had one of the most dissapointing meals I've ever had. It made for some amusing conversation but some of the dishes were basically inedible.