We like to drive route 30 across Nebraska between Ogalalla and Grand Island to avoid I80. From Grand Island we use route 34 to Lincoln and Route 2 to Nebraska City. We have also used route 36 across Missouri and Kansas.
You may want to consider getting off I29 at St. Joseph and taking route 36 and route 73/75 up to Nebraska City. Route 2 between Nebraska City and Lincoln is divided highway. There is an interesting
Lewis & Clark Visitor Center in Nebraska City just off route 2. Route 34 goes through a number of small towns including Seward, designated the Nebraska
4th of July City. We didn't know about this until we drove through on July 4, 2010. if your timing allows, it looked like a good place to be for the 4th.