From the main page, you can view Nebraska territorial and state census extractions published in vols. 9-22 of the Nebraska & Midwest Genealogical Record, the journal of the Nebraska Genealogical Society. The database includes the 1854, 1855 and 1856 territorial censuses, plus a couple federal mortality schedules at the bottom of the page.
If you’re hot on the trail of a Cornhusker ancestor, you can also browse surnames in the Nebraska & Midwest Genealogical Record name index.
A great reference to determine historical boundaries is Nebraska Counties, which has maps from when the territory was formed in 1854 to the state’s last county name change in 1925.