Coney Island is the best for everything - the beach, the rides, the beer - but mostly for the Skee Ball. It's incredibly addicting, affordable and satisfying (depending on your aim).
The Brooklyn Flea is another treasure trove of odd finds, cool artifacts, and handmade goodness. If you're looking for inspiration or just something cool to hang on your wall, you can probably find something here. And if all that treasure hunting leaves you hungry, you are in luck--there's a delicious assortment of local food vendors and artisans there too.
This is a very delicious Sandwich place in my neighborhood. I normally order the #5 - Bell' americano. It's a great sandwich. Also try the wonderful cookies.
This is one of my favorite bars in Manhattan. It has a courtyard in the middle and they only serve a large selection of Belgian beer. It's always dark with red lights so it's like a giant darkroom with everyone developing hangovers instead of film. The courtyard creates a front bar that is open on the weekends, so if you get cornered talking about architecture you can escape over to the front bar and watch people walk down 4th street.
The Bronx Botanical Garden is a place my father and I have been going to since I was a child. Here's a photograph I took of him here. It has hundreds of species of trees and flowers. Sitting in the middle of the Bronx, it's most recognizable as a green oasis from the grays and concrete of city life.