As a general rule, use the Keystone Trail as a north/south route to campus.  It is also wise to ride through neighborhoods and less busy side streets as much as possible. 

Commuting from the West/Northwest End of Town.

If you are coming from the West end of town, Maple Street is the best street to travel.  Maple street has a wide shoulder from west Omaha through I-680, and then has 2 east bound lanes and 2 west bound lanes.  Ride in center of the right hand lane.  Always use sidewalks if they are available instead of the street. Most motorists are aware that bicycles have a right to be in lanes of traffic, and will simply go around you.  You can then access the Keystone Trail at approximately 84th street and head south towards UNO.  Exit the Keystone Trail at Pacific Street and ride up the (very wide) sidewalk and enter Elmwood Park.        

Commuting from the East end of Town.

If you are coming from the East end of town, Pacific street is good west bound street to use.  Just enter Elmwood Park and head north toward campus.

Other Trails in Omaha, visit: http://www.omahatrails.com