US citizen living in Canada

Darren,

Typically, anyone can register a business in the United States by paying the appropriate fees and submitting the required paperwork to the state and federal offices involved, respectively.

Without knowing what type of business you would be operating, I couldn’t suggest one state over another. As this is a topic we come across quite often, I’d like to invite you to a previous answer I posted in reply to a Canadian citizen operating a U.S. company.