The 5* Michelin type of places aren't my forte, so i probably won't be much help in that regard, but there are some places that i like:
PIZZA: (i know a LOT about pizza, which is consistent with me not knowing much about 5 star Michelin restaurants )
Juliana's, 19 Old Fulton St, Brooklyn
==> it's not very far into Brooklyn and worth the trip, imo, as it's my favorite pizza in NYC. My advice is to arrive at 11:15am for when they open at 11:30 to avoid the lines that will be there throughout the day. Take the subway there (A or C train to High St) and then 'walk off' the pizza by walking the Brooklyn Bridge back to Manhattan as you take in the NYC Skyline. After pizza you could head towards the waterfront to the Brooklyn Ice Cream Factory if you saved any room for some homemade ice cream.
Lombardi's, 32 Spring St
==> history claims the first pizza place to open in NYC... still excellent
Adrienne's Pizzabar 54 Stone St
==> stick with the 'grandma' style pie which is what they are most known for
(NOTE: none of the places above are 'slice shops'... they are all whole pies only)
Katz's Delicatessen 205 E Houston St
==> quintessential NYC deli with sandwiches (most notably corned beef) piled high.
=====> while in this area you can/should also stop at Economy Candy (108 Rivington St) for a huge candy selection from yesterday and today (as well as lots of bulk candy/nuts... their dark chocolate covered graham crackers are my favorite (and i don't even really like dark chocolate))
Rosa Mexicana (various locations throughout NYC)
==> never had a bad meal... but too often walk out feeling like i didn't get a good value (table side guacamole is usually excellent... drinks really pricey, imo (which is maybe where i don't feel like i got a good value))
Jackson Hole Wyoming 521 3rd Ave
==> i haven't been in awhile, and service is typically hit or miss, but i always enjoy the burgers here which are HUGE. It's not for everyone, but it's walk-able from your hotel
El Rio Grande 160 E 38th St (west side of Third Ave at the base of an apartment building)
==> i can't vouch for the food as i haven't been in awhile but the frozen margaritas are really good and really strong... enjoy these at the bar with the free chips and salsa (i'd do some more research on recent food experiences then decide if you want to eat here or elsewhere... but my recommendation is based upon the margaritas and chips)
Capital Grille (although if you have one in your own hometown then maybe try something else while in the city... but if you do go, do try the lobster mac n' cheese... might even be worthwhile to eat this with a few drinks before heading out to dinner)
Peter Luger in Brooklyn, but world famous for their porterhouse (not a cut i eat, so the experience is lost on me... but if a porterhouse aficionado, may be your new favorite steak place) NOTE: CASH ONLY!!!
Wonton Garden 56 Mott St
==> hole in the wall 'noodle and soup' place, stick with the noodle and dumpling soup choices, i wouldn't order any true meals here
Wo Hop 15 Mott St
==> another place i haven't been to in a long time, but still has long lines waiting to get into this basement eatery
Turntable Chicken (314 5th Ave)
==> this place is a 'speak easy' for Korean Fried Chicken as it's not that easy to find, you walk thru the street level door and up the stairs, thinking the whole time "what am i doing here?!?"... but then you're greeted by a somewhat loud but modern restaurant featuring some excellent Korean Style Fried Chicken (which if you haven't had before is fried twice, each oil at a different temperature, and served 'hot and spicy' or 'soy garlic' (or you can mix your order between the two))
Few Higher End Places:
Atlantic Grill 1341 3rd Ave
==> another place i haven't been to in awhile... not over the top expensive but it's somewhat pricey, although they do get some very good fish the few times i have been there
Low End Place:
Chicken and Rice Cart (southwest corner of 53rd St and Sixth Ave... look for the "Halal Guys... we are different) 7:30pm-4am
==> if you're willing to venture into the 'street meat' scene, this cart is known for their $7 combo platters (chicken and lamb (which is really gyro meat)) with a healthy dose of white sauce and ask for the hot sauce on the side (as it's crazy spicy). They are actually now franchising storefront locations worldwide (they have one in NYC on 14th St and Second Ave, but i think the allure of the place is decent food from the street)
If i'm missing any 'must have' foods that you need info on let me know.
Enjoy your time in NYC!