I agree, rent a bike and cycle all around, it's easy to orientate yourself and hard to get lost.
Head out to the Great Wall at Mutianyu. You can hire a taxi for the day or get an organised tour. It is much quieter than the usual section at Badaling.
For adventure, hike one of the wild sections of the Great Wall...try Jiankou, it's so steep and crumbly. Gotta scamper up on ur hands and feet! but amazing views!
1 Day Beijing Tour for Great Wall and Ming Tombs