RDU International Airport is about 15 miles away, a simple 20-30 minute drive depending on traffic.
Aloft Chapel Hill
Aloft Chapel Hill, which is a modern-chic local Marriott Hotel, is less than 1 mile away, around 3 minutes by car or 15 minutes on foot. Includes several good restaurants and shops right nearby.
There are a variety of lovely, affordable local AirBnBs around Chapel Hill, Durham, Hillsborough, and Pittsboro.
If you're visiting from out of town, here's some places to check out while you're here:
Ackland Art Museum at UNC
Carraway Village Drive-In Theatre
Honeysuckle Tea House
Maple View Farm Ice Cream
Morehead Planetarium & Science Center at UNC
North Carolina Botanical Garden