The Alton and Grafton (Illinois) area should be nice in the Spring. You can take a more scenic route by going to St. Charles, Missouri (very close to St. Louis airport), then following the country roads towards Grafton. You would have to use two ferries, one of them costs $7 and one is free. Arrive in Grafton and have lunch at the Loading Dock (they are open seasonally so check for hours), or drive to Alton and have lunch at Fast Eddie's, which is kind of a very big dive bar and ridiculously cheap (also check hours there as they open later in the day).
The Statehouse Inn is definitely where you want to stay. You will be in walking distance to the Lincoln sites. You will definitely want to see the Lincoln Museum and allow at least 1/2 day minimum - it is fabulous! It is without a doubt the best museum I have ever been in. I'm sure you want to see Lincoln's Home, that is just a short walk from the Museum, and you might want to go into the train depot across the street from the Library. Some restoration work was done there a few years ago and my son was one of the carpenters involved in that project. New Salem is wonderful to visit (check hours as some places have shortened hours due to budget cuts). I'm sure you would want to visit the Edwards home where Abe and Mary attended parties and I believe I have read that the Edwards home is where they met. It is open to the public, but be sure to check their hours.
When you are visiting New Salem, you might want to visit Petersburg, which is just a few miles past New Salem. It is a beautiful little town with a few places for lunch. Abe's first girlfriend, Ann Rutledge, is buried in a cemetary in the Petersburg area, but I understand that it is hard to find. But, if you are interested, I'm sure a bit of internet research would help you locate it.
You mentioned the Surveying Museum, but you might want to check to see that it is still open. About a month ago, I remember hearing about a small historical museum that was being permanently closed to due the budget cuts and for some reason, I think that was it.
You are probably aware that the Frank Lloyd Wright designed Dana Thomas House is in Springfield and it is well worth a visit.
Springfield isn't known for our restaurants, but a fun place to eat is at Donnie's Homespun in the Vinegar Hill Mall which isn't too far from the Statehouse Inn.
Have a great visit to Springfield!