The Lincoln Restaurant is indeed very good. We went a few weeks ago, and had a great meal, one of the best I've had in Iowa. The restaurant does get busy, yes, but they just opened a wine bar 2 doors down, and that seems to function as a kind of very pleasant, drinking-required waiting room. And if you bring wine-bar bottles over to dinner, they waive the (extremely reasonable) $5 corkage fee.
The place seems to work like Lula Cafe-- a cheapo standards menu (sandwiches, hamburgers, etc), plus high-end chalkboard specials. The high end specials are overpriced, as chezbrad said, and the night I went there were only 3 of them, but the hamburgers are underpriced, so. I had a fancied-up pork chop, very tasty, that ran north of $30; however, my fiance had an appetizer-as-entre of a bucket of mussels, which was overfilled, and $11. And these mussels were, somewhat absurdly, among the best mussels I've ever had. It made no sense, really-- Mt Vernon, Iowa? But there they were. We also had a mountain of french fries-- why not?-- cut in-house, which were excellent, up there with Sweets & Savories'.
Which leads me to my actual Cedar Rapids recommendation: The Flying Wienie. We were tipped off by the Lincoln Cafe waitress; we'd praised her french fries, and she said, "I know, they're great, almost as good as The Flying Wienie's." The Flying Wienie is a converted gas station, decorated with airplane memorabilia/crap, painted Hot Douggy red & yellow. It has a prop plane on the roof. It's run by an ex-Chicagoan, and he serves respectable-to-excellent Chicago-style hot dogs. His fries are, indeed, outstanding. He makes barbecue, too, but eh on that front.
Also in Cedar Rapids is a very good Czech bakery, in Czech village, Sykora Bakery. It is 100+ years old, and the last time I was there, it was closed for repairs, so call ahead.
Oh, yes, Motley Cow is good too, probably the best upscale Iowa City food I've had. And if you're down that way, there is also a better-than-you'd-have-reason-to-expect Japanese restaurant, in a mini-mall: Sushi Popo. The owner, Dick, really makes an effort. Fiance and I have grown very fond of it.
You can read more about the Lincoln Cafe at their unfortunately-named website:
http://www.foodisimportant.com
Flying Wienie
103 8th Ave SW
Cedar Rapids, IA 52404
(319) 861-3036
Sykora Bakery
73 16th Ave SW
Cedar Rapids, IA 52404
(319) 364-5271
http://www.sykorabakery.com
Sushi Popo
725 Mormon Trek Blvd
Iowa City, IA 52246
(319) 338-7676