Trail Running

Since I'm trying to increase mileage I'm always looking for a change of scenery. Since I started trying to get my life in shape I'm also trying to get myself to do things I've never done before, just so that I push myself to be a better person. This past weekend I did just that - I found a change of scenery and did something I've never tried.
On Saturday my husband and I went on our first group run with the Indy Runners. This was a huge deal because it brought me out of my comfort zone and got me to talk to other runners. I'm going to do their summer marathon training and start running with them after we get back from Germany. We did just over 4 miles on the Monon Trail which was a great change of scenery for me and a personal distance record - my longest run had been 3.8 miles previously. I'm really proud of myself for getting out of my comfort zone and increasing my mileage all in the same day. I also did my first run not on a sidewalk when we ran on the Monon Trail. In and near Broad Ripple the trail covers several bridges which was pretty cool and it was great going through all the shade when running instead of just being on city streets. I'd like to try trail running but I'm still trying to find a place that is an actual trail instead of asphalt.
I'd love something a little more gentle on my legs if possible, does anyone know of any trails around Indianapolis close to downtown that would be good for running?