Indianapolis is home to many attractions of interest to the gardener or nature lover:
White River State Park http://www.in.gov/whiteriver/ which features many interesting places along the downtown Indy walkway. Be sure to visit the spectacular indoor butterfly exhibit and greenhouse at the Indianapolis Zoo and White River Gardens http://www.indyzoo.com.
The Capital City Garden Project http://www.ces.purdue.edu/CES/Marion/ccgp/index.html is one of many community efforts to bring more green to urban centers, as well as providing a way for gardeners to get involved.
Think Spring and you think of the Indiana Flower & Patio Show! In March area homeowners and gardeners attend to see the latest in horticultural products and services http://www.hsishows.com/indiana_flower_patio.
Furthermore, you can find a nearly endless range of day trips to festivals and sites of interest at the Tour Indiana site: http://www.tourindiana.org/