Can we get a 72 hour Transit permit

Flying to Singapore, from the US and getting on a 7 day cruise, Thailand and Vietnam. We get off in Hong Kong and stay overnight until 3:30 pm then fly to Beijing. We get to Beijing at 7:00 pm on the 18th of May and then fly to the Us on the 21st at 4:30 pm, so will that work for us.
I believe from what I read you don't need a permit to visit Hong Kong.
Also we have a US passport. We are trying to avoid buying a China Visa and also does the 72 hour Transit cost anything?