We did Sea Grapes on our own in late Feb 2007. Taxis are lined up ready to take you wherever you want to go as soon as you get off the tender in GC. They will fill the mini vans to the rafters before they leave. We had an AC van take us there, but no AC on the way back - it was pretty toasty. No problem whatsoever getting a cab back to town when we were ready to leave the beach.
We got to the beach just before 10 am, and rented chairs and an umbrella - I can't recall exactly, but I think it was about $30 for the lot. At the time that they situated us, we thought we had an excellent location - little did we know that the beach would get very crowded and that several people would end up in front of us - cutting off our view of the water. So, if you get there early, put your chairs and umbrella at the shoreline.
The snack shack looks clean and attractive, and if it hadn't been so hot and crowded, we would have stayed for lunch. However, after 2 hours on the beach and dipping in the ocean, we headed back to town for lunch.
I think the beach is quite a bit narrower after the hurricanes from a few years ago, but the sand that remains is lovely and soft, the water is warm and refreshing, and the kids can play along the edge. It does drop off fairly quickly. There were various water toys available for rent nearby.
The nice thing about doing this on your own is that you get to decide how long you will stay.
Have fun. Definitely get there early, and park at the edge for the best view!