The above suggestions are all great. My favorites include repeats of the above.
Local Sites that charge a fee:
*The Children's Museum is amazing. One of the best in the U.S. IMO, so it's definitely worth the trip, even with a little one. My best friend has a 15 month old, and he loves it there.
*Conner Prairie is great. A living museum with lots of farm animals and activities for young kids. Symphony on the Prairie makes for a good date night for you and DH, too.
Road Trips:
*It's a couple of hours south of Indy, but Holiday World is great fun. They have a water park that's nice for young kids. Very clean and safe.
*Lafayette is about an hour northwest of Indy, but they have a number of spots for kids, including a Wolf sanctuary that I love and a hands-on play station. Sorry, I can't remember names, but I'm sure there's info available on the parks and recreation site.
Local Free Stuff:
*The IndyParks website has the local parks to visit. My favorites are Holiday Park and Eagle Creek. The city parks do not charge admission, unlike Fort Harrison which is a state park.
http://www.indy.gov/eGov/City/DPR/Pa...ParksHome.aspx
*There are a number of greenways in Indy. I'm sure there's one in Lawrence. We live near the Monon trail which is a great place to walk on the weekends. You can meet all kinds of people. Broad Ripple and Carmel both have spots to stop for a bite to eat or do a little shopping. There are links to trails on this site:
http://www.indygreenways.org/
It's hot and humid in Indiana in the summer, so I recommend a lot of morning or evening activities when the heat isn't so bad. There are a number of YMCAs in Indy. They have great kids activities if you have a membership.
I hope you enjoy your stay here. If you are looking for friends to hang out with, our door is always open. Send me a PM, and we can exchange info.