This is a belated thanks to all who responded to my initial OP for help with my time in Beijing before and after a longer cycling holiday near Guilin.

I made minor modifications to JieJie's itinerary (multi-hour plane delay), but I did go the GW (Mutianyu, something I had thought I wouldn't be able to do) and I am so glad I did. I ended up sharing the itinerary with a couple I met one morning at my hostel who were sitting with a map and a guidebook, completely bewildered as to how to most efficiently map out and plan a day without unnecessary back-tracking. I knew just how they felt - I always get a bit overwhelmed by it all.

I knew my time was limited, but you all helped me make best use of it. I really look forward to going back (possibly next spring) because there is so much I want to explore more.

Thanks again, everyone, for all the fantastic help!