When visiting my family in Indianapolis during the twins' spring break, my sister and I took them to Butler University's Observatory and Planetarium, which is open to the public. This is a highly unusual place- most observatories (college ones in particular) are exclusive. However, when Mr. and Mrs. James I. Holcomb donated money to Butler for the building in the 1950s, the primary condition was that it available to everyone. I think after over 50 years, the staff is a little tired of letting "the great unwashed" in, but they do it regardless.
The telescope is open to the public Friday and Saturday nights- check the website for tour times. The planetarium show and tour is $3 for adults and $2 for kids (we paid $7 as a family), kids under 4 are free. Private tours and shows from groups of 15 or more can be arranged ahead of time ($50 minimum). Currently they are running a show on the moons of Jupiter, which was a little disappointing since it was little more than a powerpoint. I like my planetarium shows to be more about stars and constellations, but I suppose they are trying to provide variety for the regular visitors.
Telescope viewing is always free, but they won't open the 28-foot dome if there's even a chance of rain. As a 38-inch Cassegrain reflector (mirror) telescope- the largest in the state, it is extremely vulnerable to moisture. There are also several smaller and more modern telescopes riding "piggy-back." The whole thing is mounted on four steel beams that go all the way to the ground and held up by a concrete floor 2 feet thick to minimize vibrations.
The building itself is beautifully designed and decorated with a multi-color marble floor inlaid compass and zodiac design. Symbols for the planets and the sun are wrought into the stair rails that wind around in a rectangular spiral up to the telescope dome. (I don't think it is handicap/stroller accessible) Poster sized images of celestial objects around the lobby and up the stairs provide interesting facts.
This was one of my favorite places to visit as a kid, and I think for the price- it can't be beat!