How far are you willing to drive? In terms of riding from in Greensboro, on a bike, to long hill climbs, there isn't really anything near that length unless you're willing to pedal over an hour to get there. In terms of closest, probably:
Going Northwest: 
Hanging Rock Mtn (1.7mi, 750ft)
Sauratown Mtn (2.4mi, 950ft), easy to combine into a loop with Hanging Rock
Pilot Mtn (2.1mi, 1050ft)
Those three are all 35-50 min away by car and paved. 
 Any further and you're climbing up to the Blue Ridge Parkway, which is full of great climbs that can be 20min or more. 
If you go West, you can hit good climbs in the Old Fort area (paved and non-paved).