We also did Great Bay beach on our June12-19 Eastern cruise with our 8 year old, since we, too, did not want to take any taxi time. One hint, though, which might be helpful. After you get off the water taxi, if you go to the left side of the dock, you will notice several yellow water markers in three different areas. Although you will immediately be accosted by "get your two chairs, umbrellas, and 2 drinks for $20 here" speech, GO ON down the beach to the biggest area that is ringed by the buoys.
That is the area you can swim in. We made the mistake of taking the very first area of chairs, only to find out that the water in front of that area is marked off for the water taxis, and the area next to it for the sea doos. Just keep going a little farther before you get your chairs. (We still had a GREAT time, though- we just stayed on the sand and in the water!)