Going to the Coney Island Boardwalk is a really nice day trip. We went there a few months ago, and had a great time. We took bikes along, and biked on the boardwalk along the beach. It was a beautiful and exciting bike ride. Along the boardwalk there are lots of arcade games that you can play. And of course nearby is Wendy's hotdog countdown. There's also Luna park which is formerly Astroland amusement park nearby. It's a great amusement park for kids and adults, and famous for it's rollercoaster The Cyclone. The Cyclone is a really old icon of Brooklyn, and Luna Park kept it when they redid the park.
Getting around NYC is very easy with trains and buses. Keep in mind, that trains will get you to your destination much quicker than buses. So use trains when you have that option.
Bars and nightlife
There are many bars near the Coney Island Boardwalk. Do some research as you'll find some are much better than others.