UTMC

When I went to NYC, I stayed at Piccini's and Shifty's and ate at random pizza and bagel joints. It was awesome, if perhaps not what you're looking for.

I was just up there for work. We stayed downtown off wall street. The rooms there were crazy expensive, but the area is nice and clean. Best thing I did was just pick a direction and walk around, found more interesting things that way than I thought i would. Of the touristy things I got to do I liked simply walking around Central Park the best. Empire State Building and Times Sq was meh. Do try to get together with the locals, good times will be had.
Going to try to make it back up there in Sept for a weekend just to run around. There are some good deals on nice places to stay depending on what part of town you are wanting to stay in.

Time Square made me want to go do anything but be in Time Square.
Other than that, all of my great NYC experiences involved shit tons of booze and/or drugs, and ended up in places like NYU dorm rooms, rooftop gardens in Brooklyn, or nearly getting kicked out of the go kart track on Coney Island for ramming people (drunk, and high on cocaine).

That being said, my personal suggestion is to try all of those.
Oh, and to ask Muppet where the best place in Brooklyn is to get a burger with everything on it.

If you can avoid midtown/Times Square you won't be disappointed. Some people like being swarmed shoulder to shoulder with tourists though.

I would try finding a hotel somewhere in Chelsea, Greenwich Village, SOHO or Grammercy Park; there are a ton of "wander about" things to find all over those neighborhoods.

If you find yourself in the Meatpacking District on a nice day wandering around, check out the Highline. We just finished all the signage for it, and it's pretty damn cool. It's essentially an abandoned elevated rail line that has been converted to a public park.

Food:
Tamarind and DBGB are both pretty awesome (pricey as hell too, but most decent places are).
http://www.tamarinde22.com/
http://www.danielnyc.com/dbgb.html

Shake Shack is awesome if you're in the mood for a burger and shake in the park, but be forewarned the line can be long (it moves fairly quick though).
http://www.shakeshack.com/

Tropical Sensation is an amazing and cheap West Indian / Spanish restaurant on the Upper West Side near Harlem
https://tropicalsensationny.com/main.php

Pretty sure my couch is too small for the both of you.

There's just tons of cool shit to see and do in the city. Bring money, lots of it.

I want a bagel.

For food, a lot of my knowledge is centered around midtown and downtown since that's where I do business, but here are some good eats:

http://churrascariaplataforma.com/ - Brazilian Barbecue.

Avra
Photo
141 East 48th Street, New York, NY
(212) 759-8550 () ‎ · avrany.com
Category: Greek Restaurant - very good.

Les Halles
Les Hales, NY
15 John Street, New York, NY
(212) 285-8585 () ‎ · leshalles.net
Category: Restaurant French - good, all the way downtown

▼ Le Bateau Ivre IncAddress:Station is accessible‎
230 E 51st St # 1
New York, NY 10022-6571
Get directions
(212) 583-0579
lebateauivrenyc.com‎ - awesome beers and there is a Belgian beer bar down the street.

▼ Bridge CafeAddress:Station is accessible‎
279 Water Street
New York, NY 10038-1798
(212) 227-3344
bridgecafenyc.com - very old, very good, and very reasonable.

East is a decent Sushi chain, there are a bunch in NYC.

Jeremy's ale house, all the way downtown has 36 oz beers, cheap, outdoors, fun after-work sort of place.

If work is paying for it, I wouldn't go too nuts trying to find cheap. I don't stay in NYC hotels and my company puts guests up in the Waldorf Astoria or some other high-end hotel. I'm told the Holiday Inn Express on Wall Street is actually very reasonable (for NYC) and yet not a shoebox.