Thanks for the compliment. Do you have to be at the airport by 4.30 or flight leaves then as if the latter, needing to arrive 1.5 - 2.5 hrs approx prior (depending on if international flight or just to Hong Kong) gives you just the am for sightseeing. You need to leave 2 hrs each way for the trip from Beijing out to Mutinayu but you could get away just after 6 am to be there by 8 am (I think it is) opening. You could have 3 hours-ish n the wall and be back to the airport by 1 pm ish with an hour wriggle room. Less rush if you have to be at the airport later. Summer Palace says the garden opens at 7 am and the "scenic spots" so that would be the buildings at 9 am. It is around an hour by subway (and prob similar given traffic) by subway from central Beijing. You need probably 2 hours to walk around most of the "peak" spots plus extra if you go inside halls. We arrived at 3.30 and were sitting resting waiting for sunset away from the crowds by a bit after 5.30 so took 2 hours and of course buildings were closed. So the Summer Palace is probably more realistic as you could get there by 8.30, have a pleasant morning exploring and lots of time to get to the airport but if you aren't seeing the Great Wall elsewhere on your trip then I understand the attraction. I would be concerned with the distance getting to and from Mutianyu in case there was some major drama (road closed due to accident?) if I had an international flight to catch later that day. You could also throw Badaling which is closer into the mix.