As someone who has just moved from Las Vegas, Nevada, the district names we have for Las Vegas are either duplicative or non-sensical for the current time of the game. The three districts are Paradise, Summerlin and The Strip.

The issues are Paradise Nevada and The Strip are basically the same area as most of the Strip and the airport are encompassed within the township of Paradise Nevada. So these two could be combined into The Strip. The Strip does not encompass the Fremont Area, however, which was one of the first commercially developed and mob-run areas of the Las Vegas Valley. It was known as Glitter Gulch and it was a turn of the century area that expanded quickly and moved south later on to create what we know now as the infamous Strip.

Secondly, the area known as Summerlin wasn't even known as Summerlin until the mid 1970s, and wasn't even a registered area in Nevada until the mid 1940's when it was known colloquially as "Husite." Thus I'd suggest removing Summerlin completely in order to keep with the game's 1930's timeline. Henderson, while still a 1940's incorporation, was at least around in the 1930's and would make a better area. It also became highly industrialized as well and would have been perfect for mob related activities as well.

In conclusion, I would recommend renaming Las Vegas' districts to:

The Strip

Glitter Gulch (or Fremont, or Downtown)

Henderson

TL;DR. Las Vegas districts as currently portrayed in game are period-inaccurate. Consider renaming.

If we're looking in the general area for the 1930's - 1940's timeframe (things are pretty spread out there, so I'll do my best):

North West: Glitter Gulch (it's not really north west but the NW was vastly under developed at this time. It's slightly north and east of The Strip but not as north east as McCarran Field, next entry.)

North East: McCarran Field (the name for Nellis AFB after WWI, not to be confused with the current airport)

Center: The Strip

South East: Henderson

South West: Red Rock (Technically the west of Las Vegas but it was one of the first settled areas in Las Vegas due to the huge sandstone quarries and trafficking to California. It's rumored that a lot of bodies are hidden out that way, and up in the northwest which wasn't developed at that time at all but out in the middle of the desert.)

Geographically, the layout would be more like this:

Center: Glitter Gulch 

North East: McCarran Field 

South: The Strip

South East: Henderson

West: Red Rock