If you have a couple of hours to kill and some ambition to spare, traveling via bicycle between cities in the Triangle is a good way to go without burning increasingly precious gas. But you really do need to have time to spare—and a spare inner tube wouldn't hurt, either.
A good place to start when determining your route is to visit Web sites such as www.bikely.com, where cyclists can post their favorite routes (www.sanoodi.com is another popular site elsewhere, but has yet to gain traction in the Triangle). Also, visit www.mindspring.com/~brucewr/ec/links.html or www.gotriangle.org for more info on biking routes, safety, listservs and general information.
One route from Durham to Chapel Hill is to hook up with Erwin Road on Cameron Boulevard in Durham and follow it until you hit U.S. 15-501. From there, you can bypass 15-501 on the parallel access road Dobbins Drive until you hit Franklin Street. Erwin Road has a narrow shoulder though and can be tricky—and unpleasant—if there is heavy traffic on the road. Also, cyclists should definitely not ride on Erwin at night—in general, experiment with inter-city routes in daylight and avoid riding between cities at night, as many routes aren't well lit or lit at all.
Some good branches off of Erwin Road are Turkey Farm Road, which takes you to Martin Luther King Boulevard in Chapel Hill. Another route between Durham and Chapel Hill involves traveling on the south side of 15-501 using Old Chapel Hill Road and University Drive.
The bikely.com site has numerous cyclist-submitted routes between Raleigh and Durham (with Amtrak suggested as a return trip!), and even Raleigh and Carrboro (no trains for the return ... yet). From personal experience, I can attest to a lovely trip from Durham to North Raleigh: Starting from the Bull City downtown, hop on Holloway Street and follow it until it turns into Wake Forest Highway (Highway 98). A good place to turn off toward Raleigh is Olive Branch Road, which then turns into Leesville Road.
Highway 98 is useful to travel to North Raleigh destinations, but the shoulder gets narrow and unsteady in parts and there are cars behind you constantly—and motorcyclists like this road, too. A rearview mirror on your handle bar is especially useful on this road, as it is for most rides.