If you stay on the strip, you don't need to rent a car.
You can get a taxi to drive you from the airport to your hotel (and it's not far either as the airport is right next to the strip). Actually, a number of hotels also have shuttles to the strip, so if you go to one of the major hotels, I'm sure you can use their shuttle to get picked up at the airport and bet taken back.
There is a train that can take you up and down the strip if you want to go to a show a little down from where you're staying. I haven't been on it myself, but I know it's there.
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