Thanks for the tip Quepaz. I checked Siesta Key out on line and it does look like a good choice. In addition to the beach you would have Sarasota right there for seeing some fine art and the Ringling Museum. I am already familiar with Longboat Key, so I know it is a part of Florida that would be more what we would be looking for. And, to top it off, Dr. Beach declared that Siesta Key was the 3rd Best Beach in 2008. Hope that didn't make it too popular. I found timeshares to rent on Longboat Key, but not yet on Siesta Key.
