The way to get a different or no Las Vegas is to prevent the state of Nevada, which is not actually that difficult. Clark County remains part of Arizona, which does not legalize gambling. The cow counties go to Utah, with the Tahoe area going probably to Utah but maybe to California, again no legalized gambling.
Las Vegas is really the only non-Chinese city of its type (the Chinese like gambling) and the closest equivalents, Monaco and Sun City, where also built in geographical legal loopholes.
There two main alternatives for a sin city for Americans, and both towards the Southeast. The first is that the state of Florida legalizes gambling, at least in south Florida, in a bid to drive up real estate prices in Florida, which is pretty consistent with OTL Florida history. So Miami or some other south Florida site is the main alternative within the US. The second is that the British allow the operation to move to one of their Caribbean islands, the same way the Cayman Islands are an offshore tax haven, though it should be noted that the existence of the Cayman Islands benefits alot of British aristocratic families (for what it is worth, there are gambling casinos in London).