How would I get to Badaling from Starmoon Hotel in the Northeastern part of Beijing?

If you go to Badaling by bus, you could take bus no. 909 from East Dong Feng Bridge to Deshengmen first, and then change to bus no.919 through line or express line to Badaling.
If reach it by train, you may take bus no.701 from East Dong Feng Bridge (东风桥东) to West Pianganli Lukou (平安里路口西), then change to subway line4 to Xizhimen, get out and then walk to Beijing north railway station to take a train to Badaling.
FYI： https://www.travelchinaguide.com/cityguides/beijing/greatwall.htm

Booked a Day bus tour in Beijing, they said it was 4 hours at BaDaLi the great wall of China, and a few other stops, the cost 30RMB or 60RMB for my wife and I. Once on the way and well outside the city of Bejing we were informed it was triple the cost 180RMB for two. We were at BaDaLi for 1.5 hour then the remainder of the day, from 9am to 2pm was spent driving from BaDaLi to a Jade jewelry manufacturing Store listened to a sales pitch, then to a food store to purchase products, 15 minutes for lunch then 15 minutes at a Wax Museum my wife refused to enter and every that went inside said was not good then to another jade jewelry sales presentation. We were droped off in the middle of Bejing, walked to a Subway Station took the subway, transfered to another line, walked to a bus stop and took the bus the rest of the way home. 1.5 hours to get to where we were staying from the time we were dropped off in Beijing. I will never take a bus tour in China ever again!