The Archway is Nebraska's answer to the Gateway Arch in St Louis. The arch has lots of transportation history, and the grounds some interesting historical exhibits. A sod house, a mound house, a herd of wire bison and a maze for the kids. You can even feed the fish off the bridge on the grounds.
If you go:
This is a nice place to rest and take a break. There are picnic facilities, a gift shop, a diner and some walking trails. Plan on at least an hour or more.
Links:

Interstate 80 Exit 275
Kearney, Nebraska 68847 USA
Mailing address:
Great Platte River Road Archway
3060 East 1st Street
Kearney NE 68847 USA
Phone Numbers:
The Archway
+1 (308) 237-1000
+1 (308) 237-1000
Archway Toll-free Number
+1 (877) 511-2724
+1 (877) 511-2724