Upvote:3
I'm not sure that 1 month is counted as a layover. But you don't need to get a visa, provided you are travelling on your US passport. The only thing they may ask you for is proof that you have booked flights leaving the country, but you are covered there.
According to the Japanese Embassy in the US
A visa is NOT necessary for US passport holders visiting Japan for a short-term stay of less than 90 days with the purpose of tourism and business. *