I live in Springfield and can agree with what everyone has said here.
The Abraham Lincoln Museum (while not free) is absolutely amazing and my kids love it (youngest is currently in 3rd grade). Like others have said, there are a ton of Lincoln sites to see in the downtown area, and the Dana-Thomas House (Frank Llyod Wright) is well worth the time and effort. It has a "suggested donation", but technically is free.
I need to look back at the OP to see exactly your spring break is, but as of right now, we don't have snow on the ground, but our grass isn't green either. There is a chance of flurries tonight, but no accumulation is expected. Highs this week have been in the mid 50's, so it feels like a heat wave (with a couple of 70's in the past couple of weeks). That is still a couple of weeks away, and I hope the weather warms up a little more.
We are heading out to D.C. for spring break, and are hoping that it is warms up there too. We will barely make the beginning of Cherry Blossom Festival, and we aren't even sure they will be in bloom due to the extended cold weather.
When we went to Wis skiing last month, we took 90/94 and went around Chicago. It is a fairly easy drive.
If you have any specific questions, let me know.