If you and your girlfriend have lived together for at least two years and want to continue living together in the UK without getting married, you can apply for an unmarried partnership visa. If you do want to get married, you have a couple of options:
1. get married in the UK (though do it before Feb as the rules are changing!) on your visitor's visa and return to the US to apply for your spousal visa.
2. get married in the US (your gf can enter the US to marry you because it is not her intention to reside there after the wedding), then go to the British consulate in NYC, LA, or Chicago to apply for your spousal visa (or apply by post -- you don't have to go in person)
3. apply for a UK fiance visa (from the US, either in-person or by post), get married in the UK, and adjust your status to spouse from within the UK