I am currently in the U.S. on an L-1 visa. My fiance is Hungarian and currently visiting me on a tourist visa. My L-1 was issued in Tokyo, Japan. Can we get married in the U.S. and get her an L-2 visa without her having to leave.
You would be getting her an L-2 status, not visa, within USA. I usually discourage change of status from B visa, but it is possible to do this. Consult with your lawyers.