If you realize the subway system uses "uptown" and "downtown" for north and south bound trains it gets easier. I know this isn't exact. The point is understand uptown, midtown and downtown. Weekend schedules can get tricky so make sure you check the lines, especially if you go to one of the Central Park museums.
Some subway entrances only service an uptown or downtown train, but not both.
A good tip for knowing which entrance to take is to face the direction you want to travel and take the entrance on your right. For streets, numbers go up for uptown and down for downtown. For avenues, the numbers go from East (alphabet and 1st) to West (12th) with 5th being the dividing line between east and west on addresses (10 E. 10th Street would be east of 5th Avenue and 10 W. 10th Street would be west of 5th).
Beware, some NYC restaurants charge for ice tea refills. Really.
Don't they all? I've never seen free refills in sit-down restaurants and only at one fast food place. I highly recommend it, by the way - Rickshaw Dumplings on 23rd between 6th and 5th Avenues.
More good places to eat: Eataly, Big Gay Ice Cream, L.A. Burdick Chocolate Cafe, Kee's Chocolate, Kyotofu, Food Parc, Rice to Riches, Crumbs, Magnolia Bakery, Papabubble, Despana, Harney & Sons Soho, Garrett's Popcorn, HB Burger (just off Times Square), Earl of Sandwich, Sweet Revenge, Grom, Amorino Gelato, Chikalicious, Kitchenette, . . .
Good places to go: Highline, Top of the Rock, Central Park, Skyscraper Museum, Irish Hunger Memorial, Battery Park City (especially the Otterness Sculpture Garden), Metropolitan Museum of Art, MoMA, American Museum of Natural History, New York Botanical Gardens, Bronx Zoo, Rockefeller Center,
. . .