If you're planning a bit of sightseeing head to Deering Estate— just one of the monuments in Palmetto Bay. Hotels.com travelers also say the area is full of friendly people and has lots of nice beaches.
If you want to give your credit card some exercise, head out to The Falls shopping mall in Kendall. It's also full of great shops and restaurants, so you can spend the afternoon having a wander. Splash some more cash at The Falls.
