From the NC Maps Collection at UNC (see links to the right)
This map (above) was published as part of an atlas between 1855 and 1860. It's fairly simple and doesn't depict many of the smaller towns and crossroads in the area - perhaps unfairly catapulting Durham into the minds of readers as it still had only a couple hundred people living in is vicinity. Also it seems that the Eno got lost in the shuffle of this map though it does include New Hope creek flowing south from the Durham area.
The map above has the potential to be the earliest of the two and was published in either 1858 or 1859 also as part of an atlas. I especially appreciate the added detail though I have to say that the measuring is a bit off as Durham has been shunted almost all the way to the Orange county line and quite far south of the Eno. I'd love to know if anyone else can find an earlier atlas or large scale map that depicts Durham