He doesn't need to do anything to marry you in the US as long as he doesn't plan to live in the US after the wedding. He just comes in as a visitor without a visa, you get married and then apply for a spousal visa. You'll just need to check with your local court house what their procedure is for getting married.
A lot of people do it this way because it means one less visa to apply for (no need to switch from a fiancé visa to FLR(M) and you can work immediately on a spousal visa, while it's illegal to work in any capacity on a fiancé visa until you have received FLR(M).
Ultimately though, you should do whatever is best for your personal situation - for example, do you have specific reasons why you might wish to marry in either the US or UK (I.e. Dream location, certain family members who you want to attend but can't travel etc)? Do you wish to be able to work immediately when you move? Will it be cheaper for him to fly to the US for the wedding, or for you to get a fiancé visa?
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