I also live in Indianapolis. One thing I have to disagree with is our zoo..it's tiny and not worth the price. Of course, I grew up in Cincinnati which has an amazing zoo that you can spend days at. The Indy zoo is like 2-3 hours tops.
Conner Prarie is great, we love it there. It's on the north side of Indy.
Incredible Pizza Company is a large arcade place that's really fun. Our "older" nephews, ages 9 and 12, love when we take them there. You need to go hungry since you have to buy the buffet to play there, the foods decent though, not fine dining but serves it's purpose. There's 2 locations, I've only been to the Greenwood one but there's another closer to downtown.
Indy has an AMAZING children's museum. It's huge and has so much to see and do.
Our downtown is beautiful, and a walk by the canal is lots of fun.
Tibbs Drive-In is really fun if you're into watching movies. A lot of people think the area around the drive-in is bad, but don't worry. You're safe there
If you're into exercise the Monon Trail is great.
Indianapolis also has some great parks and aquatic centers with indoor pools and slides, very inexpensive too. Here's you a link.
http://www.indy.gov/eGov/City/DPR/Amenities/Pages/Indy Island Aquatic Center.aspx
That's all I can think of off the top of my head. Hope it helps!