5 best restuarants( any cuisine) within 5 blocks of 56th and Lex.
A lot in the area.. here's a list to get you started..
BLT Steak (I've never been)
Bobby Vans Steakhouse (never been to this location)
Le Cirque (I've never been.. assume there would be breakfast/lunch/brunch/dinner options here)
Aquavit (is it still open? tasting menu + pri fixe options)
Brasserie (only been for breakfast.. a power breakfast spot for hedge fund types)
Indian restaurant row: Ada, Yuva, Dawat, Chola (Chola is well regarded on Chowhound I think?)
Four Seasons (Joel Robuchon, garden wine bar, power lunch, I assume a brunch option)
Serafinas (breezy lunch/brunch)
David Burke Townhouse (61st.. brother went and loved it last week)
Shun Lee Palace (overpriced chinese food..my expense account delivery place..)
Houstons (just tossing in a cheaper option for you to be aware of, similar price to serafinas would imagine)
The Modern (perhaps too far?)
I didn't rank which of these are best etc. but if had to pick 2 that I would like to hit if i had to choose.. Acquavit, Burke Townhouse. I've dined at Acquavit but never had their tasting menu, which I need to get off my butt and do if they are still open...though that wouldn't work at your $60/limit dinner option. Never dined at Joel Robuchon's place either, but that wouldn't fit $60/person.. but perhaps the new garden will work (www.fourseasons.com/newyorkfs/dining/the_garden.html). Steakhouses can be done at $60/head although my experience at BLT Prime is that can exceed $60/head easily.
www.menupages.com for a place to look at menus for all of these places.