"Times Square South" is a little misleading, but the hotel is nice
Probably if they gave the location as "Hell's Kitchen" it would hurt business. This hotel is a hike from Times Square, but the price is fairly reasonable for NYC and we always enjoy Hampton Inns when we travel for leisure. Our room overlooked 39th St. It was decently sized by NY standards, very clean and comfortable. Although it was New Years Day, things were kept relatively quiet and only one or two street persons came into the lobby looking for snacks. Everything we wanted to visit was walkable from here. 
If you are a Hampton fan and want a decently priced room in New York, consider this as one of your better options. Don't let the location turn you off.