I moved from NYC to Philly recently, and I can honestly say that I felt a lot safer in the vast majority of Manhattan, Queens, and Brooklyn at all hours of the night than I do here. Of course, my only experience in the city was during the late 90's and this decade--my father was there on business constantly during the dark ages of the 70's and especially the 80's, and says the difference (especially in Times Square) is absolutely unbelievable. The areas you mentioned are incredibly commercialized, and you will be not be hassled at all, except by the guys handing out flyers for strip clubs and sample sales.
NYC has the best public transportation system in the country--24/7 access by bus and subway to anywhere you could possibly want to go. (Unless maybe you want to go to Staten Island, but don't worry about that, because you don't. Even people who live in State Island don't want to go there.)
BTW--the one thing I don't agree with 280plus is getting to the city from the airport. If your business is comping it, just take a taxi; the air shuttle and switching in Flatbush (or is it Jamaica?) is a pain. But I strongly agree with him that you should get a laminated pocket map and an unlimited weekly metro pass. Also, the BBQ place he's referring to is most likely Virgil's, and I heartily second his recommendation. They have one of the best beer lists you've ever seen.
If you're going to have a lot of walking around time, check out Wall Street, the Village, Tribecca, Soho, 33rd, 42nd, Times Square, Lexington around the upper 50's, and Central Park. If you only go to one famous restaurant while you're there, skip the tourist trap that is Tavern on the Green and go to DeNiro's joint, the Tribecca Grill, especially if you're a wine drinker. The wine list comes out in a huge binder, and IIRC correctly their collection is rated four or five stars by Wine Spectator. If you like Chinese food, skip the crowds of China Town and take the 7 to Main St in Queens. You can't go wrong with Joe's Shanghai (try the steamed pork soup dumplings, but poke a hole in them with a chopstick and let them breathe for a minute. One of the wait staff's favorite hobbies is waiting for a white guy to shove a 400 degree dumpling in his mouth.)
Edited to add answers to some questions you actually asked
The rolling bag isn't a bad idea, although usually only women use them. If you're walking at all, even the most comfortable shoulder bag will seriously leave a dent in your shoulder. If at all possible, just keep it in the hotel room or at the office. As for cash, you'll only need it on the street--even the vending metro card machines take plastic (something I sorely miss here.) And EVERYONE in New York has some kind of accent, so don't sweat that.