My wife and I visited Omaha last weekend and had a wonderful dinner at the Flatiron Cafe. It's a few blocks away from the official boundary of the Old Market at 17th and Howard, but worth the detour.
The menu had some really unusual combinations, but they generally worked. My wife had a special of halibut prepared with mostly Asian style vegetables, but served on top of a potato latke, of all things. (The latke wasn't the best I've ever had, but it was certainly passable.) I had cinnamon-marinated chicken in a sundried cherry BBQ sauce with a side of sauteed fingerling potatoes and pears. Absolutely delicious. Some interesting wine selections as well, including a surprising sparkling red that was very tasty.
Only complaints were that the desserts in general didn't seem to have quite the "Wow!" content as the other courses in terms of creativity. We had homemade German chocolate cake, which was certainly fine, but not as exciting as what came before it. And the bread had a smoked flavor (probably a smoked cheese of some sort) that wasn't really what I look for in bread.
We thought price was an excellent value for the quality, at least compared to fine dining restaurants in other cities. The two entrees (which come with excellent mesculun salads--another unusual touch in this class of place), an appetizer, a dessert and two glasses of wine came to less than $80 (before tip).
Thanks to those on this board who recommended this restaurant!