Do we need a China Visa if stay two days in Beijing and two days in Hong Kong? We are US Citizens.

Hi, I am traveling with my husband. We are US Citizens. On our way back to US from a trip from Singapore we would like to stop two days in Beijing to visit the Great Wall, then make another stop of two days in Hong Kong for sightseeing, then flight back to US. Do we need to apply for a China entry permit in advance or we quality for the 72 hours free transit. We will flight between cities and we will have hotel reservations ready.