The mainstay of any field trip is the local museum, and the Indiana State Museum offers a wide variety of programs for educators. An alternative venue that also caters to hands-on education is the Children's Museum of Indianapolis. It offers discounts at various times throughout the school year as well as programs specifically designed for home-schooling. Rounding out the mainstream possibilities are the Indianapolis Zoo and White River Gardens Park.
Indiana State Museum
http://www.indianamuseum.org/educators/
Children's Museum of Indianapolis
http://www.childrensmuseum.org/teachers/visit.htm
Indianapolis Zoo and White River Gardens Park
http://www.indyzoo.com/content.aspx?cid=370
The most memorable experiences happen when you stray from the mainstream. The Historical Landmarks Foundation of Indiana has several educational walking tours of the city that are designed to fit with the state historical curriculum requirement. You can also visit the historic Morris-Butler House, which offers hands-on learning about 19th century lifestyles and etiquette for both children and adults.
A trip to the doctor isn't something to look forward to, but a visit to the Indiana Medical History Museum taps into the appeal of the weird. Housed in the 19th century Pathology Department Building, you can tour pathology laboratories, autopsy rooms and even a library of abnormal specimens.
If you really want to get down and dirty with the past, however, then visit the Connor Prairie Interactive History Park. It takes hands-on learning to a new level, with educational re-creations of many 19th century crafts.
Historical Landmarks Foundation of Indiana and Morris-Butler House http://www.historiclandmarks.org/Resources/Classroom/Pages/FieldTripsTours.aspx
Indiana Medical History Museum
http://www.imhm.org/index.html
Connor Prairie Interactive History Park
http://www.connerprairie.org/
If you're looking for something really unusual, you might try visiting the Exotic Feline Rescue Center. One of the largest exotic cat rescue centers in the United States, this charity provides permanent homes for illegally imported, abused and/or abandoned exotic felines. It currently houses almost 200 tigers, lions, leopards, cougars, bobcats, ocelots and even one female tigon (tiger/lion hybrid). Located about an hour outside of Indianapolis, this location is a bit harder to get to, but definitely worth the trip.
Exotic Feline Rescue Center
http://www.exoticfelinerescuecenter.org/home.html