A block north of the wedding venue is the world's largest children's museum. So many permanent and rotating interactive exhibits, you'll hardly have the time or stamina to see it all. Should be interested or have restless kids, it's worth checking out. (Heads up, admission is rather expensive, investigate their website to see if you qualify for discounts for student, military, etc.)
Right across the street from the downtown hotel block, is an excellent museum. Probably less engaging for kids under age 6, but still very interactive and significantly less expensive than the Children's Museum. Probably less engaging for kids under age 6, but still very interactive and significantly less expensive than the Children's Museum. Heather went to the State Museum for the first time last summer and LOVED it.
Emphasis on the park. It's a wide open space on the western edge of the densely packed downtown metropolis with art and a nice view of the river. It's got the canal walk (please don't expect San Antonio Riverwalk) which runs past the Indiana State Museum, the NCAA Hall of Champions, and the Eitlejorg Museum of American Indians and Western Art. Best of all enjoying the state park is FREE!
Fun fact: Indianapolis has the second highest concentration of monuments to veterans per capita (following Washington D.C.). There are a ton of monuments scattered across downtown, but the Indiana War Memorials takes the cake. It's got a museum in the basement of Indiana's role in most American wars. If you're feeling extra patriotic the majority of the memorial's tower is devoted to a somber reflection room with the biggest American flag I've ever seen.
I have never been to the Speedway Museum. It has been the largest sporting event for the city for over 100 years, and even as someone not enthusiastic about motorsports, the 500 is known to be exhilarating for all. Since May is racing season, April would be a good time to visit (probably, like I said, I've never been).