The Virginia B. Fairbanks Art and Nature Park: 100 Acres This former quarry has become a place to admire modern art among woodlands, meadows, wetlands and a lake. Seasonal guided tours run on weekends. (317) 923-1331; imamuseum.org/100acres 
Indianapolis Art Center The center offers interactive exhibitions and artist demonstrations, both indoors and in a 12-acre creativity park. Indianapolis Art Center 
Congressional Medal of Honor Memorial, Indianapolis A glass wall in White River State Park honors recipients of the nation's highest military tribute. Each day at dusk, the memorial's sound system plays recorded stories of medal winners and the conflicts in which they fought.
Indiana War Memorials, Indianapolis Climb 330 steps to the top of the 1902 Soldiers' and Sailors' Monument (left) for a 360-degree view of Indy (or ride the $1 elevator). Also nearby are the Indiana War Memorial Museum, Indiana War Memorial Plaza, Veterans' Memorial Plaza, USS Indianapolis Memorial, University Park and American Legion Mall -- all free.
Falls of the Ohio State Park, Clarksville You can see one of the largest naturally exposed fossil beds along the Ohio River in Clarksville (about 100 miles southwest of Cincinnati, just across the river north of Louisville, Kentucky).
Fossil collecting is not allowed, but you can explore up to 220 acres of fossil beds. Naturalists lead hikers across the beds from June through October, when the river is low and you can see the imprints of creatures from more than 380 million years ago.
For a fee, you can also visit the blufftop Interpretive Center, which shows a movie recounting the area's history.
Whitewater Gorge Park Trail, Richmond A popular 3.5-mile hiking trail goes through downtown Richmond (about 75 miles east of Indianapolis) to Thistlewaite Falls, a bird sanctuary, vertical cliffs, Happy Hollow, Weir Dam and an old flour mill.