Crime has been down overall. I would judge New York City as pretty safe. Common sense will keep you safe. Right now the hot borough is Brooklyn this due to the rapidly gentrifying neighhborhoods along the L train. Williamburgs is the hipster capital and if you are gamer and like to drink I would recommend Barcade, a bar with old school arcade games. Very charming. You will also find cool vintage clothing stores in the neighborhood. Beware some will rape on price.
The great thing about New York is that whatever your are into there is something to do. I'm not into the club scene at all so I will not be able to help there but there are tons of options there. My interests are dining, art, bookstores and cafes, parks. Below are some my favorites. Google these for directions and such.
Dining and Food
Momofuku Noodle Bar and Momofuku Ssam. If you love pork you will love David Chang's cuisine.
Balthazar's. In the heart of Soho. Great ambience and food. Steak Tartare is the best I've tasted. A little pricey though.
Shake Shack. Great burgers and shakes located in Madison Square Park.
Minca. Awesome authentic ramen spot in the East Village. Great prices.
City Bakery. Another good brunch spot.
Murray's Cheese. On Bleecker. Knowledgeable staff. You can ask for free samples of cheeses from around the world.
Union Square Greenmarket. Open Mondays, Wednesday, Friday, and Saturday in Union Square. Great organic produce, meat, poultry, and cheeses.
Art
The Met. Try to visit twice. It's too big to see everything in one day
MOMA. Recently went through multi-million dollar renovations. Worth seeing
Cooper Hewitt Design Museum. This museum is devoted to design--graphic, furniture, interior, product, you name it
Also look into the various art galleries located in old warehouse building district in Chelsea--west 20s
Bookstores and Cafes
The Strand. Various locations.
Housing Works Bookstore and Cafe
Starbucks--Ha, just joking. But they're great for the restrooms. Protip for those not familar with NYC. The lack of publicly available restroom is pain. Use Starbucks. They're everywhere. Mickey Ds as well. Barnes and Nobles have great public restrooms and Whole Foods have clean and accessible restrooms.
Parks
Central Park Duh. Rent a bike or rollerblades.
Washington Square Park. Looking for weed, here your spot. I kid. But its true from what I hear. There some great food carts here too.
Fort Tryon Park. All the way up in Inwood. There is a bus that takes you straight there. Amazing view.
Battery Park. You can take the Staten Island ferry. It's free.
Geeky Stuff
Forbidden Planet. Comics, Toys, T-Shirts, and other geeky goodness
Toy Tokyo. Vinyl Toys, capsule toys, big ass toys
Final tips
Get a subway map and an unlimited Metrocard. Much more affordable than taking cabs everywhere.
Don't be afraid to ask strangers directions if you are lost. Best bets are cabbies. They know the city inside and out. If you ask someone besides a cab driver make sure to at least ask more than one person for a second opinion. People sometimes give wrong directions.
New Yorkers are on the run. Dont' take it personal.
Don't stand in the middle of the sidewalk; move to the side to avoid foot 'traffic'.
Times Square sucks. Maybe except for the shows.
Hot Dogs suck. Well the ones from the carts. They are boiled, not grilled. Yuck.
Favorite neighborhoods.
Lower East Side, Flatiron, Harlem--don't be afraid, and Chinatown.
Other Boroughs
Bronx. Not too bad as some people may have you believe. Try to catch a ballgame at Yankee Stadium. Beachers seats are decent actually. The Stadium will be gone two years to make way to new stadium they are building next door. Bronx Zoo and the New York Botanical Gardens are worth a look
Queens.
The most diverse borough, ethnically speaking. Home to great, cheap ethnic restaurants. Try making stops along the 7 train for some good Mexican fare. The best Mexican food is found in Queens. Manhattan Mexican joints just suck.
Staten Island.
Can't say.
Brooklyn.
Walk over the Brooklyn Bridge. You'll have an amazing view of the city. After that you can have some ice cream at Brooklyn Ice Cream Factory and a pizza at Grimaldi's.
Enjoy,