I'm sure you can find something w/in cycling distance. I think the whole town is w/in cycling distance unless he really doesn't like to ride far! There are some big hills in town if he's trying to avoid that. The Carrboro route is usually less hilly in general, but it depends on the neighborhood. My DH walks to his UNC office or takes the bus, but he usually walks for the exercise.
Chapel Hill/Carrboro is very small compared to Boston, so pretty much anywhere in either town is bike-able, I'd think. I'm not sure I'd want to bike from more outlying areas like Durham or Hillsborough to UNC, but I'm sure there are some die-hards who do it.
There are lots of cyclists in CH/C, though, so he'll have plenty of company. The towns are pretty bike friendly although there's always room for improvement. There are bike lanes on many of the main roads and some dedicated bike paths away from the roads, too.
Like RhiOrion said, CH/C has a good bus system and the buses are ALL FREE and very popular with lots of students and faculty as well as just folks about town. They're not skanky at all. My kids are still thrilled at the prospect of riding the bus on an outing. (They don't ride the school bus.)
We do have two cars, but parking on campus is a big pain in the butt and DH rarely drives unless he's got to go somewhere else that day (like to the kids' school for a special celebration or some other event). I'd say he drives to work once a month or less, so I think one car is totally doable. It would be better for you to be the one with the one car, though. My kids love the bus, but it's easier if it's Daddy taking the bus to and from work rather than trying to wrangle all the errands and kid stuff and groceries, etc on the bus. We do use the second car on the weekends and evenings when we go in different directions.