North End Grill may be worth checking out.

Angelo's in little Italy or

Osteria Laguna
209 east 42
 have fun , Pollie  

...but not mid day as it is packed. The earlier you get there the better. They open at 8am. Or go in the evening but that can be dicey as well. You must get pastrami on rye. IF you don't want to get that then don't bother. BTW, the sandwiches are huge with a price to match. This is not fine dining but it is quintissentail NY.

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For delicious French food in a fashionable, buzzy downtown setting -  
Dirty French (in the Ludlow Hotel)
Cherche Midi (282 Bowery)
Lucien (14 1st Avenue #1)

If you want to get splurgey in midtown Cafe Boulud and Le Bernadin are both tough to beat on both a culinary and design scale.  
The Modern (Midtown) is one of my favorites. The dining room is formal and looks out on to the sculpture garden of the MoMa (modern art museum), the bar room is very chic, but without the white table cloths. Both are fantastic.  

Good thai can be tough, but my current favorite is Qi in Williamsburg. Don't miss the kama sutra dolls in the bathroom

Good casual (fairly healthy) lunch spots - Dimes, Jack's Wife Freda, Seamore's...

Here are my favorite guides for current NYC hotspots. They're both put together by NYC locals - designers, restauranters, hoteliers, etc.  

http://www.nytimes.com/interactive/2015/09/11/t-magazine/new-york-city-travel-guide.html?rref=collection%2Fcolumn%2Ft-city-guides&action=click&contentCollection=t-magazine®ion=stream&module=stream_unit&version=latest&contentPlacement=4&pgtype=collection&_r=0

http://www.thecitiphile.com/citiphiles/

Enjoy, and feel free to message me for more tips xx

Brunch : Boqueria (tapas) in UES, Esperanto in East Village

Dinner : BLT Prime

If you try these, let me know what you thought about them!

PJ Clarke's in midtown for dinner, Katz's Deli in the East Village for lunch are two of my favorites.  Head to Little Italy downtown if Italian food is on your list.  Capital Grille on 42nd Street in midtown is also a fine choice.  Then again, sometimes it's just best to leave your hotel, and explore the places nearby...