The Chelsea Market is filled with great restaurants and speciality food stores and pop up shops. I love stopping in and getting a gourmet grilled cheese from Lucy's Whey or a healthy juice from raw food restaurant One Lucky Duck, while shopping for dinner ingredients at the Italian market Buon Italia. For a great sit down restaurant, I love The Green Table, which serves great farm to table food.
Best pizza in NY. Be prepared to wait. Check to see if they are shut down by the health department or tax collectors before going. Get the square pie with pepperoni and hot peppers.
Within an couple hours' drive of NYC, you can find lots of sleepy seaside towns. Not only can you get your soft ice cream and salt water taffy on, but you can still spot cool, hand-lettered signs and other relics of a past generation's amusements.
Hands down the best wood fire pizza I've had in Brooklyn. Great for a date or if you're feeling fancy schmancy. (Also, don't sleep on the caesar salad here.)