Nebraska honors Kansas concealed carry permits. Do you have one? If not, you can't carry concealed up here regardless of the Alpine Inn's status. I can understand why you wouldn't have one now that Kansas is a constitutional carry state.
Also, be careful about the City of Omaha's handgun registration. It applies to anyone who brings a handgun inside city limits and doesn't have a permit that Nebraska honors. I doubt the police would bother someone passing through with an unloaded handgun in the trunk. However, if you plan to stay for a day or two and don't have a permit, you would technically be in violation of the registration ordinance. It sucks, but that's the way it is. The current mayor, who has her own permit, would like the state to completely preempt local gun restrictions.