There are no "closed cities" in the United States. Even Oak Ridge, Tennessee is an open city, although certain of the Department of Energy facilities locate there are "closed" to the public who don't have sufficient security clearances to enter them.
There are several "abandoned town" in the US where trespassing might be charged if a person enters them without obtaining a permit to do so or is not a resident. They include:
- Treece, Kansas ( across the state line from Picher,OK and now only has two residents)
- Cardin,Oklahoma (abandoned)
All of the above are Environmental Protection Superfund sites due to contamination from lead and zinc mining done in the areas in the early to mid 20th century. All are posted and visitors could be arrested if they enter without permission or refuse to leave when instructed by authorities.
Mercury, Nevada isn't a city or town. It's a government construct made for the purpose of housing people who work at the Nevada Test Site. While the Wikipedia article for it refers to it as a "closed city" this is incorrect. Access to Mercury by the general public was never possible as it only exists because of the site; it is not an organic city. Russian "closed cities" invariably existed prior to the their being closed