I think it is not enough to go to both in one day. You may see Badaling and Ming tombs in one day with a taxi. It is over 70km between Mutianyu and Badaling, more than 2 hours on the way.

Thank you for the information!

Could you please let me know how long it takes to get to Mutianyu by taxi? What about Badaling? Is there basically one route to each? Are there toll roads that may make the journey faster (if so, how much is the toll?)?

Thanks to everyone here, by the way, for posting and answering so many questions! This site is a great resource.

Perhaps 1.5 hours from the city center (for example Xidan, Beijing Railway Station, etc) to Mutianyu by taxi. No more than one hour to Badaling if no traffic jam. Toll road will be faster. 919 bus express line also go through toll road. The toll fee is about 25-30RMB, cheaper if you go from the west part of downtown Beijing.