I made a really long list, but several have been mentioned so I omitted them. I have a ton of more things to add, so hopefully I'll have time later.
Food
My three favorite steakhouses in the city are
Strip House,
Peter Luger and
Keens. Cannot go wrong with any of the three.
Rocking Horse for slightly upscale and wonderfully tasting Mexican.
Craft is a la carte everything, and you can pick just about anything on the menu and not be disappointed. Also has a very impressive wine list.
Neptune, which I've mentioned before, is my favorite seafood restaurant in the city.
Gramercy Tavern has already been mentioned, but so worth mentioning again. My favorite restaurant.
Two Boots Pizza is a love it or hate it pizza place. I love it. I believe their East Village location shows movies.
San Loco for cheap, delicious Mexican.
Bars
MJ Armstrongs is my standby for watching sports. Great wings.
Union Hall has a lot of space, bocce ball, live music, two floors, an outside garden, and a fun, young crowd.
Jimmy's Corner is an interesting bar. Located in Times Square, it's the complete opposite of touristy. Jimmy, the owner, used to train Ali and was one of his corner men. He's there almost every night and it's a fun place to stop by for a few beers.
Bohemian Hall & Beer Garden is a great place to spend a summer evening. It has probably 50-75 picnic tables outside with a pretty good Eastern European beer selection. My weekly poker game moves here during the summer.
Iridium Jazz Club is meant to be visited on a Monday night, when Les Paul and his trio perform. Something that must be done once.
79th Street Boat Basin is another place to grab a beer in the summer. It's strange, NY is surrounded by water, yet there are very few places to hang out on the water. This is one of the few.
Everything Else
This is just some random stuff I came up with.
Chelsea Market is an amazing place to shop for food. Period.
Strand Books is my favorite bookstore. You'll find a new favorite book everytime you're there.
Smith Street in Brooklyn was already mentioned - one recommendation on that street...
Smith & Vine is a small wine shop, but the owners are passionate about wine and carefully choose their inventory. I've heard they recently moved down the street and now offer a wine bar.
Vintage New York is another favorite wine shop, but for a different reason. They only sell wines produced in NY State. You'd be surprised with some of the good wines offered, especially those from the Finger Lakes Region. I know the Upper West Side location has a tasting bar.
The Central Park Boathouse is a nice place for brunch. Afterwards, take a row boat out on the pond.
Brooklyn Art Museum always has interesting exhibitions. Afterwards, hit up the Botanical Garden and take a stroll through Prospect Park.
Bryant Park offers free movies in the summer, but get there early. The link is to the 2006 schedule to provide an idea of the types of movies shown. Grab a blanket, wine and some friends and it's a good time.