Worth Avenue is a beautiful and historic shopping area to go for a walk and take a look around. At the end of the road you will find the beach by the clock tower which many families love to take pictures and sit on the beach.
The Society of the Four Arts Garden
2 Four Arts Plaza, Palm Beach, FL 33480
This is a smaller botanical garden that will take about 20-30 min max to get through. I suggest getting a sandwich at Buccan beforehand as well.
Palm Beach Lake Trail
South Lake Trail, Palm Beach, FL 33480
This is an amazing biking or walking trail right by the water (5 miles long). If you want to rent a bike I suggest going to Palm Beach Bicycle Trail Shop (Address: 901 N Dixie Hwy, West Palm Beach, FL 33401)
Mounts Botanical Garden
531 North Military Trail, West Palm Beach, FL 33415
This botanical garden is about 15-20 min away from the hotels.