If you are raising children, Indianapolis is a great choice! I used to nanny here and there is always something cheap to do with your kids. Let me elaborate-
The biggest children's museum in the country is located in Indianapolis. This is an excellent place to visit, even for adults, I always learn something new and it's also home of one of the largest Chihuhly (blown glass) sculptures in the world. PLUS, a family membership with unlimited access for up to 6 people is only $88.
The Indianapolis zoo. I have only been here with the kiddies a few times but it is reputably a forward thinking green type zoo. The animals are in natural habitat enclosures, etc, etc. Very fun. The penguin house it divine.
The new public library was just finished downtown and it is once of the most beautiful buildings! It is basically one old neo-classical style library linked to a 6 story modern glass edifice by this amazing glass atrium flanked with steel flying buttresses. I love the library. The children's wing is an amazing place called playscape. They conuct daily story times and there is a planetarium!
Not to mention the Indy parks system rocks!
The art museum also has a really world-class collection.
The farmer's market scene is exploding and it is possible to get delicious organic produce inexpensively. The farmer I work for runs a CSA the website is here-- www.homesteadgrowers.com
Broad Ripple or Meridian Kessler would be my plugs for neighborhoods you should look at. Fountain Square is nice, but still feels unsafe to me at night.
All of this comes to you from a girl who was born and bred in small town Indiana, then moved to San Diego for a few years, then back to Indiana, settling on Indianapolis. I also take frequent trips to Chicago and Nashville, however, and would probably dislike Indy if it were more isolated, so to speak.
Gee, I hope this helps a little!