Although it was 10 years ago, I also stayed in Greenpoint at the
Box House, a boutique hotel. We had a duplex loft apartment for 4 people which was reasonably-priced at the time. Their regular rooms are currently around £180 per night based on a sample 8-10 night check for March. I thought it was a very pleasant option, and it still seems to be well-regarded (4.5 TripAdvisor, 8.6 Booking.com).
Article about it (a few years old).
It's an easy journey across to Manhattan; the East River ferry terminal and subway are both around 8-10 mins walk.
I appreciated being out of the hustle and bustle and you get some great views across the river. Both Greenpoint and Williamsburg were quite charming, and I enjoyed strolling down to Williamsburg Bridge.
Never walked so much in my life as on that trip though!