I'll most likely be coming up from San Diego and will try to get a couple of others down here to come with me as well.

I go to GenCon each year and know some people in the area, usually go a few days early to hang out and do things.

Some things I can think of are a couple art museums, one being the actual Indianapolis Museum of Art and the other is the Native American & Western Art Museum. Not everyone share my interest in museums though. They also have a zoo, I have never been to the zoo (being from San Diego most other zoos don't impress me much), but it could be worth checking out for a day. There is also a mall right next to the convention center if shopping is a desirable activity.

The convention is fun or exciting even for people who aren't gamers, at least for a day. And just checking out the Con together could be fun on it's own. There is a lot of casual gaming aside from the more serious stuff as well.

Definitely would recommend getting a hotel downtown though, walking most places isn't terribly far if you do and parking is a hassle otherwise.