Given the new rules governing marriages between UK nationals and US citizens (there's a thread concerning this at the top of this area of the forum), it may be cheaper for you to marry in the US. Once you marry, you can get an entry clearance visa to enter the UK as the spouse of a UK national from your nearest British Embassy in the US if you chose to live in the UK. Basically, you can no longer come to the UK on a tourist visa (which you would get as you are a US citizen) and marry. But you are, of course, free to marry anywhere in the US.