Suggestion for a hotel or B&B near, but not necessarily in, Springfield? The hotels there all look pretty depressing. We're only in town one night in August.

It's sounds like you're trying to avoid the chain hotels for something unique? Several of the chain hotels are fine for a night's stay, but, of course, they're not unique.
You might consider the Pasfield House, a B&B. I've never stayed there, but have walked by it many times, and it is a very old home with a lot of character, and attractive grounds. It's very close to the capitol.
The Statehouse Inn is right downtown Springfield, and has a sort of South Beach retro modern vibe, free parking and breakfast as well as an on-site cocktail lounge.
http://www.thestatehouseinn.com/
The RiverBank Lodge is a half hour-ish north of Springfield. I have stayed there and didn't give it a glowing review at the time, but that was based on the fact that I was traveling on business and needing things like good internet, an iron and room temperatures I could adjust to my needs. If none of those are of concern to you, it's a cute little family owned place with an onsite lounge/restaurant that has pretty good pizza!
http://www.riverbanklodge.com/
I guess it largely depends on what you'll be in Springfield for!
The Flagg Farmstead in Sherman, IL is a really nice bed and breakfast. Check out their reviews on TA. It is VERY clean, the owners are awesome and you get free tickets to the Lincoln Musuem if you ask for them when you book. My husband and I stayed there earlier this year and loved it!