Hi Dave: We have an apartment on the upper west side and go to New York extensively. It is an extremely safe city. Your location is excellent and you can walk to many venues, including the theater, shopping, Central Park, etc. We also highly recommend using the subway and busses - get a Metro Pass if you are going to be there a few days and want to get around easily. You can put any amount of money on it and it works on all busses and subways and you get transfers free from one to the other within 2 hours.
If you want to go to the theater, check out the half price ticket booth just north of Times Square. TKTS. They post all the shows that have seats available and they are at half price for that day's performance. They open at noon generally.
We highly recommend Carnegie Deli - everyone should eat there at least once on a trip to NYC. The pastrami is fabulous and try the cheesecake. Be prepared to be very full!!!
Also our favorite restaurant is Capsuto Freres - an easy cab ride just south of Canal on Watts and Washington.
THE BEST STEAK in the US in our opinion is at Peter Lugar in Brooklyn. Make a reservation if you want to go and get a cab to take you. It is on Broadway just across the Williamsburg Bridge and you won't go wrong.
In your area also are BLT Steak and Gallaghers. Also the Palm.
If you have time the Metropolitan Museum is wonderful. Their cafe is also great. Fifth Avenue is shopping. Big stores like Macy's are 33rd. (And by the way, Macy's has a great casual restaurant in the basement that is inexpensive with good food). If you go to Macy's stop at the Visitor's Desk on the mezzanine for an out-of-towners pass that gives you extra % off all purchases.
You can also take the bus or subway up to the upper west side and just walk Columbus and Amsterdam and check out the little shops and restaurants. Lots of choices there. A very reasonable Indian restaurant is Mughlai at 75th and Columbus.
After dark, be cautious as you would anywhere you would travel. I would not walk Central Park in the dark alone. But, NY is as safe or safer than any major capitol we've visited in the world.
ENJOY!