If you prefer newer areas with lots of development, shopping, restaurants, apartment complexes, etc... I'd recommend the areas around Southpoint Mall (I-40 & Fayetteville). This is quite close to where you'll be working, so the commute would be less than 10 minutes.
If you like more urban, hip areas with loft living and/or quaint older homes, check out the areas around Brightleaf Square, American Tobacco & Ninth Street near downtown Durham. Tons of awesome independent restaurants, bars, and stores in the area, and it would be about a 15-20 minute to work.
If you're looking for a scene more akin to uptown Charlotte, you'll want to check out downtown Raleigh. The commute will be closer to 30+ minutes or worse depending on traffic, but its the most city-like part of the region.
Hiking, biking and outdoor activities are all around. Durham in particular is bounded on the northwest by Eno River State Park, on the northeast by Falls Lake (hiking, boating) on the east by Umstead State Park (in Raleigh just past the airport - hiking, biking), and on the southwest by Jordan Lake (hiking, boating), and it is intersected by a great urban biking/walking trail, the American Tobacco Trail. There are also countless regional parks around which offer boating, biking, hiking, etc...