Indianapolis has some pretty good non-pavement running trails. I suggest you either head a little north of downtown to Butler University. From Butler, you can access the Canal Towpath; a beautiful, nearly traffic free, crushed limestone path that is roughly 3 miles if you head south towards 30th Street, 3 if you head north towards Broad Ripple.
http://www.indygreenways.org/canal/centralcanal.htm
Another great option if you need to get in a longer run: Eagle Creek Park. This is one of the largest municipal parks in the country and is on the west side of Indianapolis.
http://www.indygov.org/eGov/City/DPR/Parks/List/Eagle+Creek+Park.htm