Bedbugs were found at the Waldorf so any hotel is susceptible and not just in NYC. Check those mattresses when you get your room and put your suitcase on a rack. July...it can be hotter than hell. If you like heat and humidity, you'll be very happy visiting NYC in the summer.

If you plan on going to Broadway theatre at night, staying in Times Square will be such a huge convenience. There will be PLENTY of people on the street. Like any other place, just follow your common sense regarding safety. Keep your purse closed while outside and walk like you know where you're going. Given the numbered grid system of streets, knowing where you're going will be easy.

As for neighborhoods convenient for tourists (looking at Priceline), think of Times Sq, Central Park South, Midtown East, and Midtown West. These areas are all in midtown Manhattan. The Upper East Side and UWS are residential and might be out of the way for you. The same goes for downtown.

Like asking people for recommendations about where to go for good pizza, you're bound to get all kinds of advice here.