For off-road, the best drives would be a place just east of Lynville In. called Interlake Property. It is a great place to ride 4x4s or ATVs, or fish.
Here is a link for more info.
And don't forget Wolf Park near Battleground. They have a large wolf pack and several lone wolves and coyotes. They also have a herd of Bison and have "Wolf/Bison" demonstrations.
Great twisty scenic ride is St. Rd. 62. runs parallel with INT 64 down south. Get on at Hwy 145 and follow East make sure you stop in Leavenworth at the Overlook Restaurant and the Dock on the river then continue on to Corydon. Straightens out some after that but still scenic all the way to New Albany.