If you are looking to stay in the heart of Hanoi, there are a lot of options. We stayed in Hanoi Guesthouse. We paid around 20 dollars a night for a room and found that good value. Breakfast was nice (bread options or soup). In addition, we found the staff quite friendly. We actually booked our Ha Long Bay trip through the hotel with Oriental Sails and were very happy with their recommendation.
The location is great. There are good eating options nearby (try the Kangaroo Cafe just down the street) and honestly, I can’t see why you would stay anywhere else for the money. Recommended.