Cat Ba Island
Larger size picture here
The best way to avoid the group tours of the bay is by taking the passenger ferry from Haiphong to Cat Ba Village and then hiring out a small fishing boat for just yourselves when there.
Worked well for the most part except that our boat engine broke down and then we got lost for 4 hours in the dark because all the small islands look the same at night. Not quite the perfect plan but we still had a good time.