Do not eat near the Met, it's overpriced. Instead, walk across the park to the west side. Maybe grab a burger at Shake Shack on 77th and Columbus or, if you want to sit down, go to Kefi, a fantastic Greek restaurant, on Columbus and 85th. If you're eating dinner in that part of town, consider Calle Ocho on Columbus b/w 81st and 82nd.
the shake shack on the UWS is just mediocre, they just can't recreate the goodness from the Madison Square Park location. I don't spend a lot of time around central park on either end, but subways make it super easy to get around.
Some fun FREE things to do.
1 - walk across the brooklyn bridge and eat at grimaldis (it is really hard to find your first time) then take the subway back
2 - staten island ferry for good views of the statue of liberty. The financial district is pretty lousy for food, but if you have a subway pass, you can stop virtually anywhere and grab a bite. Stop at the WTC and battery park.
3 - The Met, followed by a walk across central park, and then the Museum of Natural History. both places have a suggested donation (of around $20), but you can give $0 or $5 or whatever you want.
4 - time square/Rockefeller Center. I know you are staying at the MM, so you probably already have this crossed off. Something you need to see once and then never go back.
Some fun PAID stuff:
1 - circle line cruise, do a twilight cruise around the city and get some amazing city views
2 - top of the rock OR empire state building. Both are pretty cool to get a great view of the city
3 - Broadway show. This is so fun in the city. At 2pm on 46th you can go to the TKTS booth and get discounted tickets for a broadway show that night.
Cheap Food I always eat when I go to NYC:
Shake Shake (the Madison Square Park location)
Ess a bagel (51st and 3rd avenue)
Pomme Frittes (2nd ave and St Marks) - place is tiny and only holds a few people
Rice to Riches (Spring and Mulberry) (in Soho) (not exactly cheap, but worth a visit once)
other cheap places
Momofuku noodle bar (11th and1st ave)
Hide-Chan Ramen (52nd and 2nd ave)
Taim (11th and waveryly) this is a falafel place
Tasty Dumpling (on Mulberry across from Columbus park) you can get 5 dumplings for a little over $1. Best thing ever when you are drunk
and of course Ray's for Pizza. There are about a million different Rays in the city and my favorite is the one at St Marks Place.
other places to try:
Katz (I thought it was overpriced $15 for a pastrami sammy)
Yonah Schimmels (to try a potatoe knish)
gem spa for and egg cream (try the chocolate) yes this place is like a little corner store
corner bistro - another great NYC burger
Margon - a cuban place on 46th right down the street from your hotel. The cubano is excellent and if you want to get crazy try some octopus salad
peter lugars - if you want to go all out and eat an amazing steak and spend a lot of money, cash only and it is in brooklyn.
Bouchon Bakery in the columbus center. It is on the 3rd floor I think and has some sweet views of central park.
Amy's Bread on 47th and 9th ave (probably 3 or 4 blocks from your hotel). Nice to grab a quick muffin or something for breakfast if you can't make it to a bagel place
H&H bagel right on the Hudson river down 47th.
Russ and Daughters on Houston (how-ston) street, great bagels with lox or smoked salmon
I don't spend a lot of time around midtown or near central park, so I don't have any food recommendations for that area, but the subway is your friend and you can take the 4-5-6 (goes down Lexington) pretty easy. Hells kitchen which is pretty much straight west of you should have some good food, but someone else will have to give you those recommendations.
If you are looking for desert. The is a max brennan (all kinds of chocolate) at union square, a juniors (cheesecake) in the basement of grand central, or a lot of different gelato shops (Il labraterio de gelato ... meh in my opinion), cones which has delicious ice cream, or you can probably find something good.
