Yes, NY is safe. It is a walking city and do enjoy!!!
Just do not walk through the park at night...alone. There are a couple areas to avoid at night.... downtown in the Bowery. Folks above have given you great suggestions. I worked across the street from the Hilton too and totally agree with Anne's comments. You may want to also enjoy some restaurants in areas other than where you will be staying as some of the trendier restaurants are in Tribeca, the meatpacking district, and Greenwich Village.

NOBU uptown or downtown
Victors Like Anne recommended
MOMA restaurant Like Anne Recommended
JoJos
Sushi Samba
Rosa Mexicana
Dylan Prime or Devin Tavern: Tell them Andi and Doug sent you if you make reservations (Tribeca)
Zoey's (Greenwich Village)
Blue Hill
Blue Fin (Times Square)
Postria
Spice Market (Meatpacking District)
Paris Match
Pastis (Meatpacking District)
Chinatown is fun
Little Italy is fun too

I'm sure you will meet folks to join you. I hope you have a great time.