For a beginner with some elevation gains at that mileage, I recommend hiking to Charlie Bunion on the Appalachian Trail from Newfound Gap parking lot. It's 8 miles round trip around 1,000-1,5000 feet elevation gain. If you have the energy do a side trip to Mt Kephart, also known as Jump Off, it will add an extra mile to your trip. The view from Jump Off will show the entire Appalachian Trail on this section of the Park. I do recommend getting an early morning start, because it going to get crowded in the late afternoon from motorists and other tourists.