If it's your first time in New York and you want to be in the "centre of it all" without being in Time Square I'd recommend
Park Central Hotel, basically 2-3 blocks north to Central Park, 2-3 blocks south to Times Square. Good (but pricey) restaurants near by, decent room sizes by New York standards.
Having said that the last time I was there for work I stayed at the
Holiday Inn in the Financial District. The hotel itself is nothing special, it's fine, but the elevators take a while. But I found the neighbourhood to be much, much less hectic than Midtown. Walking distance to the Staten Island Ferry/battery park area, decent selection of old bars/taverns in the area and just felt a lot less Disney than midtown.
I've never stayed in Brooklyn, but I'd likely book my next personal trip to that area, the bits of seen (Brooklyn Heights in particular) feel a lot more "yes I can see how people live their lives here" compared to Manhattan.
