Las Vegas doesn't have a high and low season the way many other locations do, partly because of its status as a year-round tourist destination. You can find an apartment at any time of year here. However, be sure to give yourself about six weeks to do an adequate and thorough search.
Showing a landlord that you're in Las Vegas to work or study is very important. First, you should be willing to sign a long-term lease. Landlords here have to deal with a lot of people coming to town on a short-term basis, and are looking for stable renters. Second, if you have a job or have been accepted to school, it shows that you're serious about living in the city, and not just another person hoping to be the next famous professional poker player.
Las Vegas is well designed to shuttle people around who fly into town, and this is something the locals can take advantage of. Many people walk the Strip, but if you need to travel elsewhere in the city a bus is usually the way to go. The Regional Transportation Commission of Southern Nevada operates them. If you want to drive, which many of the locals do, just be sure to stay away from the Strip, as it is almost always subject to terrible traffic jams.
Las Vegas caters to people's every desire. Essentially, whatever you could imagine doing here, you probably can. Hit the strip for great food, great shows, or great gaming. Don't overlook the other things Vegas has to offer, like world-class golf just outside the city. There is also a lot of great hiking just outside the city, such as what you'll find at Red Rock Canyon.