I can't help you with the lobstering, but I spent several months in the Abacos two years ago. It is a great area, easy navigation and unless a norther comes through great sailing.
Don't miss Hope Town, it is great for at least two days. Nice beaches, snorkeling, good restaurants,
Great Guyana Cay is also popular. If you are traveling with children or don't want to be around heavy drinking, pass on Nippers a popular beach side restaurant/bar. The beaches are nice there too.
We really enjoyed our visit to Green Turtle Cay, but you have to go through a passage called the Whale to get there and under certain weather conditions it is impassable in a sailboat. You don't want to get trapped by the weather.
Here is a link to a photo blog of our trip down the ICW and our stay in the Abaco's. It will give you some idea.
It is a great place. Have fun.