There are no direct flights between India and Las Vegas. Though several connecting flights can be taken from almost all international airports, some of them stopping at Mumbai or New Delhi before leaving the country. At least one stopover or change in flight occurs in either Europe or in the US itself. Carriers like United Airlines, British Airways, Virgin Atlantic, American Airways and several others provide services along the routes.
You can apply for a tourist visa for the United States at your nearest US Embassy. Basic requirements include proof that you are staying for only a limited amount of time, proof that you can financially support yourself during your stay and also proof that you have social or economic ties in your country that will ensure your return. You can confirm all the other documents required at the US Embassy's website.
Las Vegas is served by mainly 2 airports. The largest of these is the McCarran International Airport, which is it's main airport and is one of the busiest airports in the world. Dozens of international carriers connect Las Vegas with Asia and Europe, and of course America. The Henderson Executive Airport serves mainly private and chartered flights.
Travelling by car to Las Vegas for the weekend is a favourite activity of people in the nearby Californian cities. The Interstate 15 comes from California into Las Vegas. It is paramount to drive safe since it is a very long stretch of speeding cars, and one mistake could lead to a massive pileup. People coming from Phoenix take the Interstate 40 before joining the Interstate 15, and from the north connect to Interstate 15 from Interstate 80.
Las Vegas' public transport is really well connected. You can easily save on transport costs by sticking to the buses that run in the city, especially if you're planning to do your major travelling along the Strip or Downtown. These buses are air conditioned so it becomes even better during the hot Nevada summers. Taxis are fairly cheap as well, but the infamous Las Vegas traffic will make your commutes very long. Also a convenient way to move up and down the Strip is the monorail.
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