Visiting from Panama
You didn't give a lot of information about type of restaurant you'd like, and that's not a neighborhood I know a ton about. If you want Italian, I love Felidia over there, but it's for people who appreciate subtlety in Northern Italian cooking, and their secondi are not as great as all the things that come before.
Aureole might be a good place for you, or check out BLT Steak or if you want so spend some money, Atelier at the Four Seasons Hotel. (I did not have good food there, but many many people think it's fabulous so you should judge by searching around here)
There is also fantastic extremely spicy chinese food at Grand Sichuan, but it is not a "nice" restaurant, and you have to be willing to study up on what to order. However, if you like spicy food, you should try it.
Going uptown from there are some options, like Sushi of Gari or Etats Unis.
Sushi of Gari
402 East 78th Street, New York, NY 10075
243 E 58th St, New York, NY 10022
135 West 42nd Street, New York, NY 10036
L'Atelier de Joel Robuchon
57 E 57th St, New York, NY 10022
106 East 57th Street, New York, NY 10022
242 E 81st St, New York, NY 10028
I am not crazy about Felidia, I have to say, though I do like Northern Italian (subtlety and all). Then again, I only gave it the one shot, and when I came away completely unimpressed, I never went back. I remember ordering the beet risotto (crazy though this may sound, mine is better) and a completely unmemorable secondi (pork?), and the service we received being aggressively uninterested. I really wanted to like it, though, and would give it another try--what would you particularly recommend (no shellfish)?
Definitely seconding Etats-Unis--It has a special place in my 'hound's heart for being the first truly wonderful meal I ever ate in NYC, and I am torn between wishing it received more attention and being selfishly glad it has remained something of an underdiscovered gem.
I had just the opposite feeling about our one experience at Etats-Unis many years ago. I couldn't understand what all the raves were about since the food we had was uninspiring. The seating was very cramped (obviously necessary in such a teeny space), but on top of that, the mismatched chairs were exceedingly uncomfortable. (Looking at their website recently, I noticed that they now have matching chairs.) It's not in our neighborhood -- we went there after a visit to the Met Museum -- but even if it were, there was no incentive for me to go back. The original chef/owners, a father & son team, sold it a while back. So, it is possible the food now is different and, perhaps, better.
I also have popped in to Etats-Unis once or twice a year, and I have always had a nice time and nice food (and I don't generally pay attention to who is cooking where, unless it's to explain a sudden change that I notice on the plates)
(The most recent visit a month or so ago, my little table for two was subjected to a multi-error service nightmare, but the room seemed to be functioning smoothly and everybody seemed happy except us, so I'm chalking it up to bad luck and not jumping to the conclusion that we were being singled out personally for a bigotted reason.)