My father is from Fremont, Nebraska, a city about a half-hour outside of Omaha, so I feel the need to chime into this. Spent I many a summer in Nebraska, and even first played D&D there, with a Red Box my grandmother bought and my brother and cousin.
Lincoln is more or less a college town with the state government headquartered there. The football remarks are true -- that stadium is the center of the town on fall Saturdays. It's kind of a weird experience, one to which you must subject yourself at least once, though it was much better 10 years ago when Nebraska would kick the crap out of any team that came to Lincoln. It's a nice place, kinda folksy to some degree. It reminded me quite a bit of Columbia, Missouri, where I lived for a year in college, and is a total midwestern college town.
Omaha is really spread out. I'm from Minneapolis, which is technically about the same population (though our two largest burbs, Saint Paul and Bloomington, are big in their own right, much bigger than Council Bluffs), but all the businesses up here are in skyscrapers. Downtown Omaha, however, is relatively flat. Distances across town are long ... anyhow, there is (or was, at least when I was a kid) a great gaming store in Omaha, the Dragon's Lair.
Weather: mild winters, summers become quite hot. Pretty good overall, but this is from my perspective -- I live in a snowdrift. The winds some wintery mornings can be pretty damn nasty, especially outside of the cities, where the land is flat and featureless.