Most people seem to forget that Springfield is actually the capital of Illinois, not Chicago.
Personally I find this place to be quite boring, but if you were a visitor-here is what I would show you:
-The Dana-Thomas House designed by Frank Lloyd Wright in 1902
-Oak Ridge Cemetery
-Washington Park (I used to live a hop skip and a jump away from this park and now I live near it again. Very excited to start feeding the ducks again!)
-There are also some really cool old bookstores downtown, amazing places to eat, and nice places to sit and people watch.
-I don't think I've ever let a friend visit Springfield without trying a horseshoe at Dublin Pub or swinging by Krekels for a delicious cheeseburger & milk shake.
So I guess that's about it, unless you enjoy consuming copious amount of alchol...in which case you can pretty much walk in any direction downtown and find a bar.