This is America and you can sue anybody, anywhere, anytime for anything. However, the cost of a lawsuit is usually the stopping point. Legal fees can easily be $50 to $100k for this sort of suit.
You did not say, but are these websites related to mugshots.com? There are quite a few threads on this forum from this month about their posts which you can read. Perhaps they will give you some idea on the direction your actions should take.
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You should not post anything online about this matter, nor should you speak about it with anyone who is not your lawyer.
I have dealt with Internet-related torts; my firm's website can be visited at www.francelawgroup.net.
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It depends on the structure of the website since many are exempt from lawsuits. Speak to an attorney who provides free consultation. I don't see many taking such a matter under contingency so be prepared for a quoted fee.
The response above is not intended as legal advice since it’s impracticable to provide thorough, accurate advice based upon the query without additional details. It is highly recommended that one should seek advice from a criminal defense attorney licensed in your jurisdiction by setting up a confidential meeting. Moreover, this response does not constitute the creation of an attorney-client relationship since this message is not a confidential communication because it was posted on a public website, thereby publicly disclosing the information, which is another reason to setup a confidential meeting with an attorney.