I'm not familiar with Texas, but I spent a year in Omaha and my wife and I both loved it. I found the best steaks I ever had (and I've had a few), a huge, really fun zoo (ranks even better than San Diego some years), the College World Series, and a nice city that was very clean and spread out. There was so much to explore that my wife and I never saw (such as an art museum and some gardens). There were statues around the downtown area with a Western flavor (buffalo, covered wagons, etc) that I found strangely endearing.
People were friendly, and there were plenty (but not excessive amounts) of social things to chase if you were single. There is a nifty Market District that hosts farmer's markets in the summer and is packed with restaurants, people, artsy stuff, jams, flowers, fresh fuits, and vegtetables. They have a summer Arts and Crafts Festival there that showcases woodworking, painting, musicians, glasswork, more food, leather work and pottery.
The airport is small, but clean, neat and very efficient. Don't expect a direct flight for practically anywhere. You'll always be getting routed through Chicago O'Hare, Denver, Dallas, Atlanta, etc.
It was archetypal. Think classic American midwest locale, with baseball fields, hamburgers, hot dogs, ice cream, lots of American flags, and huge fireworks shows on the Fourth of July. Offutt Air Force base is nearby so you get to see some military vets, too. Very family friendly.
I thought the worst aspect was that it got darn cold in the winter, and the snow wasn't soft, fluffy, or thick. There was this harsh wind that seemed to pack the snow down and gave rise to this deathly, dangerous, slick ice.
As far Lubbock is concerned, I don't know because I've never been.
