If you plan to stay in town all weekend, Victory Field is the home of The Indians - Indy's minor league baseball team. Check the schedule online for some Summer games!
If you're looking for a place to take a stroll or enjoy a nice kayak on the Eagle Creek Reservoir, Eagle Creek Park is the perfect place! It has several trails taking you around the reservoir.
A little dive bar in the area if you are looking for a drink after the ceremony.