144 visa free confirmation

hello, i've been reading everything I can and think i should be good but want to double check to be sure. I am a US citizen and will fly to london to stay for 5 days before flying direct to beijing where I will stay in Hebei for 3 nights before flying out of Beijing to the US with a stopover in South Korea. Is that fine? Also, am I prohibited from driving to Zibu in Shandong for a day trip?