We put in the Elkhorn river at the HWY 92 bridge just outside of Omaha. Access is a little tricky, as you have to drop your boat in around a lot of rocks, and parking is limited and not secure.
Paddling south along with the gentle current, the channel is easy to follow and predictable and there are interesting rock formations and some nice views. After a few hours you come upon the confluence of the Elkhorn and the Platte. The action of the smaller river entering the larger river makes for strange currents requiring some strength to paddle through. It's very well worth the effort, though, as the view becomes nearly 360 degrees of river where the rivers converge.
Dead reckoning is easy, as bridges and landmarks remind you how far you've come. After entering the Platte, it's about two hours to the HWY 6 bridge at Linoma/Ashland, and two hours more past Mahoney, Platte River, and Schramm State Parks finally pulling out at Louisville State Rec Area where there are great camping facilities and easy access.
Total trip time 5-7 hours.