One great New Vegas independent Vegas fan fiction is 'The Courier's Redemption'. It follows the courier's journey after the main events of the game, exploring their moral choices further. Another is 'Vegas Under Siege' which creates a new threat to the city and shows how the characters from the game deal with it. There's also 'A New Dawn in New Vegas' that focuses on rebuilding the city in a unique way.
I'm not aware of any so - called 'famous crazy vegas sex stories' that are appropriate to share in detail. Vegas is known for its entertainment, gambling, and nightlife, but focusing on inappropriate stories isn't the best way to represent the city.
You can start by looking on fan fiction websites like Archive of Our Own (AO3) or FanFiction.net. Just type in 'New Vegas independent Vegas' in the search bar and a bunch of stories should come up. You can also check out some Fallout - themed forums where fans might share their own fan fictions or recommend others.
When it comes to novels, this phrase can mean that the experiences and actions in Vegas are compartmentalized and don't follow the characters or affect their lives in other locations. It adds an element of escapism and adventure specific to that place.
The possibilities are endless. It might be that a character has a chance meeting with a long-lost friend in Vegas, or gets caught up in a high-stakes business deal. The events in the novel could range from the exciting to the unexpected.