Below are details from two of the better maps maps of colonial North Carolina which show the area where Durham is located today (I've added a very approximate X marks the spot). The first map was published in 1733 by Edward Mosely from real reports and surveys of the colony. The second, published in 1770 by John Collet shows the remarkable transformation of the area in fewer than 40 years. The earlier map features a lot of empty cartographic space in the central and western parts of the state punctuated by a few depictions of wild animals and Native American villages (note Acconechee, now site of Hillsborough) as well as the famed Catawba trading path. By 1770 hundreds of new settlers had come to the central part of the state and set up mills and farms, some of which Collet names on his map. I'll have more on the area before 1800 in later posts but for now this trove of early maps at the North Carolina State Archives will have to suffice.
Full Size (From the Library of Congress)
Full Size (From NCSA)