How about finding a nearby club for a contest? Great way to challenge yourself and develop new skills. Marion County Fish and Game comes to mind on the north west side.
There's a lot of alleys in Indy. People usually just pick one and aim for the trash bins at the end. You can only stay a few minutes at a time before moving to another one. Sometimes you'll get a stray cat walking by if you like moving targets.
There's some good places a little south of Indy. Hoosier Hills Rifle and Pistol Club in Columbus, Indiana. You have to be a member of know someone who is a member. Go to one of there competitions and that will help get your foot in the door. There is also Atterbury in Edinburgh, IN. You could shoot at Clay pigeons to change it up. They have trap and skeet.