Las Vegas is a city on the west of the USA in the Nevada state.
Las Vegas is a city in the west of the USA in the state of Nevada.

You could also shorten it by saying "in the western US". You can use USA, but most people use just 'US'.

It is an administrative center of the most southern county of the state – Clark.
It is the administrative center of the most southern county in the state - Clark.

Technically, you can say 'of the state', but 'in the state' in this instance sounds much better.

The city is situated in a central part of the Mojave Desert.
Medved pointed out it should be "the central", but that's not necessarily true. Since it's a "part", you can safely assume that there are other parts. The question therefore becomes whether there are other "central" parts to be considered, or whether the other "parts" are not considered to be central. It's complicated, but suffice to say "the central part" does sound better than "a central part" in this instance, just as Medved said.

It’s population is over 500 thousand people.
Its population is over 500,000 people.

"Its" is a possessive, "it's" is a contraction for "it is". Also, it might not be breaking a rule, but generally it's best to stick with one way of writing numbers. Therefore, you can write 500,000, or you can write five hundred thousand. But 500 thousand looks a little sloppy.


Las Vegas is one of the biggest world entertainment and gambling business center.
Las Vegas is one of the biggest world entertainment and gambling business centers.

If it's "one of" something, that something has to be plural (e.g. один из центра versus один из центров).


Great number of casinos, hotels, daily concerts and shows attract tourists all over the world.
There is a large number of casinos, hotels, daily concerts, and shows that attract tourists from all over the world.

Two of my corrections are stylistic in nature (meaning technically you weren't wrong, but the way I wrote it sounds better)--"large" number sounds much better than "great number", and unless you're writing for a newspaper it's considered more proper to include a comma before the last item in a list of things.

There are totally more than 80 casinos, several thousand of slot machines, great number of luxurious hotels in Las Vegas.
There are more than eighty casinos [in total], several thousand slot machines, and a large number of luxurious hotels in Las Vegas.

I'm not sure what you meant by "totally", but if you meant всего/в итоге (I think those are the phrases), it's better to say "in total", not totally (the way you wrote totally makes it sound like полностью).

Also, it's generally considered better style to write small numbers out rather than using numerals (writing "eighty" looks better than 80).

The main casinos and hotels are situated in the historic city center along Fremont street in the Downtown. The most lively street of the city calls Las Vegas Strip or simply “The Strip”.
The main casinos and hotels are situated downtown in the historic city center along Fremont street. The most lively street of the city is called the Las Vegas Strip or simply “The Strip”.