The bride spent many cross-country practices on the Monon in high school, and it remains a favorite for the bride and groom today. This awesome walking / biking / running / blading trail extends through the city with many spots to hop on and off, so search for one near you. (FREE)
This memorial stands at the center of Monument Circle and is arguably the most popular symbol of the city. If you want to view Indianapolis from the top, you can climb the stairs for a nominal fee (though it's worth noting that it gets HOT up there, so if it's a steamy day you may want to pass on this one).