I'll tell you this: hotels in downtown Manhattan aren't cheap at all. And almost none of them are terribly big or newly renovated. So accept and swallow the $200/night bill, and find a good location. I've used www.kayak.com for travel bookings, since it searches all of the online sites.

Also, dont get on the subway unless you're really sure what you're doing. I know it like the back of my hand, but not everyone does, and especially not tourists.

Central Park and anything north of that area isn't the best place to be after dark. Probably shouldn't get a hotel there either.