Looking for a budget, good hotel in NYC?

I don't think you have any chance of finding what you're looking for, not in Manhattan or Brooklyn. You might be able to stay at a hostel for that price, but even the cheapest dive hotels are usually more than $50-60 a night (and they won't have Wifi).

There are subway stations all over - no matter where you stay, you'll probably have pretty easy access to one.

$390 for a week in Manhattan? Ain't gonna happen - no way, no how.

In Brooklyn? In your dreams.......

Well, I think Pod 39 Hotel will be a perfect choice for you. It is a 3-star hotel with free wifi. The one night cost of the hotel is $ 137. It is located near the Manhattan and easy to catch the metro from here.

I am sorry but you have zero chance of getting a room in NYC for $390 for a week.