I feel like any Las Vegas equivalent has to be completely dominated by gambling et al; if the vice can't push everything else out, everything else will push the vice out or at least into a smaller-scale red light district, out of moral panic and concerns over organized crime.
The Midwestern center of population is around the Great Lakes, so it has to be in driving distance of there, but I don't know how close it can realistically be; my initial thought is that an alt-Oak Ridge built near or in Paducah to take advantage of the Kentucky Dam could work quite well (likely to be relatively depopulated after the war, lots of nearby young servicemen/technicians to provide an initial seed market, copious amounts of cheap power and water like Vegas OTL, and experienced bookies etc. from the Kentucky Derby) - on the other hand, Kentucky gambling laws are strict enough that it might be worth moving it over the river to Metropolis, IL, which hosts a major casino IOTL though only since 1994.