The plot of such a fanfiction could be really interesting. Harry might be in Vegas for some kind of international wizard - Muggle relations mission. While there, he gets caught up in the Vegas lifestyle. He meets a person who is either a wizard from a different culture he's not familiar with or a Muggle with a strange connection to magic. They get married in Vegas, and then the story could explore how their different worlds collide. For example, if it's a Muggle, how does Harry introduce her to magic? And if it's a wizard, how do they handle the cultural differences between their magical upbringings? There could be a lot of humor and drama as they navigate their new relationship and the secrecy that might be required in the wizarding world.
Well, in a 'Harry Potter Marries in Vegas' fanfiction, it could start with Harry being frustrated with the wizarding world's formalities regarding relationships. He goes to Vegas for a break and gets drunk. There, he meets a girl who seems to understand his struggles. They have a wild night and end up at a wedding chapel. After the marriage, he has to figure out how to incorporate her into his life in Hogwarts or wherever he is living at that time. Maybe she has some magical abilities he doesn't know about at first.