Many of the hotels have a tennis court. You can use this by yourself or you can make a reservation with a tennisprofesional to just play a set or two or to give you a tennis lesson.
There are several horse ranches on the island. You can explore Aruba on horseback in a totaly different way, see the sights you cannot get to by car and really enjoy nature.
Aruba has 3 golfcourses. The best known is Tierra del Sol, located near the California Lighthouse. This is a very luxurious 18 holes golfcourse with a great restaurant, bar and a nice shop. If you want to play golf less expensive you can go the the golfcourse at San Nicolas. And there is a 9 holes golfcourse called Divi Links. This golfcourse is located next to the chamber of commerce at the low rise hotel strip.
Bowling is quite popular in Aruba with local teams competing abroad regularly. Shoes, accessories as well as snacks and drinks are available.
Also very populair is baseball, several teams compete and many younster try to hit the best they can. There is the well know Aruban baseball player Sidney Ponson.