I found using the WAX Bus very convenient going to the strip and back to the airport. It picks up at Terminal 1 and drops off next to the MGM. On the return, it picks up next to the Tropicana. It runs about every half hour and the schedule can be found on their website.
Note: The website says you can purchase a one way ticket with a credit card, but the machine at the airport would not sell the $2 ticket. So please have two one dollar bills because the driver cant make change. In my case, the driver was nice and allowed me to ride for free because I didnt have time to go back into the terminal and get change after we realized the $2 ticket couldnt be purchased there