IF push come to shove, Nebraska started keeping death records about 1906.
Are you flying or driving ??After you learn the library's location consider if you are going to pay all day parking or walk a few blocks. Library you want the third floor-see help dest to get oriented: http://www.omaha.lib.ne.us/hours.htmhttp://www.omaha.lib.ne.us/hours.htm
I concur with the recomendation of the Dale Clark Library in downtown Omaha.I'm told and about to see for myself that the cemetery records there are prety good.They have books and microfilms.Bring lots of dimes for the copy machine and quarters for the microfilm copies ... they are C.O.D. A portfolio to keep them in is recommended. Organize a notebook for each family up front. Computer Internet access to your favorite Geneology places like this is free but your passwords are your own risk.They have a subscription to ancestry.com, but it was messed up when I was last there.I was told they are working on it. Printouts are a dime per copy payable on the honor system down stairs. A couple of evenings a week, some very helpful ladies come to clip obits, but they also answer whatever questions they can. The newspaper IS at the Omaha library or on microfilm there.
Now you've goto t get some air sometime.Check out these website while you are still home for other places to go.
IF your search takes you to SARPY county, the Sarpy County Historical Society has additional records on file see above website under museums for this one other possiblities. Omaha has two Family History center staffed by VERY helpful volunteers.