If you are interested in a Halong Bay Tour, but have limited budget, you should definitely consider Cat Ba Island as your base for exploring the area. There are many tours and cruises you can book online, but the cheapest options are definitely the ones you can book yourself without any middle men.
There are Halong Bay tours available at most hostels in Cat Ba for the price between $12 – 15 per tour (as of February 2016). This one is an offer of Full Moon Party Tour Viet Nam, but it covers more or less all the stops that other tours do (offered by the other hostels).
Things to note: these are not expensive tours on nice cruise liners, but regular boats take take up to 20-30 people. You get to stop at a number of different places throughout the day. The food served is mostly some local delicacies, but don’t expect a Michelin star experience!
Here is a quick map of Cat Ba Island obtained from one of the local hostels (it has all the boat tour routes marked!)