Cape Florida Lighthouse
As part of the Bill Bagg's Cape Florida State Park you can take a tour of the lighthouse at 10:00 am and 1:00 pm. You can bike and kayake in the park but frankly this is a lovely beach so my favorite activity when I'm there is swimming, sunbathing and snoozing. It's a peaceful atmosphere and if you hit the beach on the right* day you almost have the place to yourself.
*People often ask me what's the least crowded days of the week to best enjoy the theme parks and beaches. From my experience I've found non-holiday Monday's and Tuesday's to be the most peaceful and laid back. Even the restaurants around here are less hectic and on those days. If you're planning a long weekend forget taking Friday off, go for the lazy Monday every time.