One of the most fun things we did was drive the Tom Cars but the company, Green Zebra, is no longer there.
We only spent 1 week in Aruba in 2009 and 4 of those days were dive days with nothing else planned, as we never really knew when we were going to get back from diving. We didn't rent a car so were dependent on the activity/tour company picking us up from resort.
One day we did go horseback riding which takes you along a scenic trail, including the beach. One day were the Tom Cars. Both were 1/2 day activities.
There are also ATV, 4 WD Jeep, and Safari tours - check those out as some take you to the same sites, mainly along the north coast, but you can be off road which is really fun. Day sailing/snorkeling is also an option. There is (was) an aloe factory which you can tour (we didn't fit that in.)
Most of the tours take you to the hidden gems of the island.