Another option:

The Las Vegas city bus #108 and #109 both run north from the airport to Sahara Avenue. One runs on Maryland Parkway, the other on Paradise St. Both cross Sahara Ave and you can get off there. Just tell the bus driver where you are going when you get on, they will help and tell you what to do.

At Sahara Ave you get off the #108 or #109 and catch the Sahara Express (SX) bus west, it runs out Sahara Ave all the way to the Summerlin suburb and goes right by the La Quinta Hotel. The La Quinta Red Rock is located at 9570 W. Sahara Ave, about halfway between Ft Apache and Grand Canyon streets, on the north side of Sahara Ave.

The bus ride will take longer than a car/cab ride since it will stop along the way, but the price is cheap, I think it is less than $5. Just tell the first bus driver where you are headed and he'll give you instructions and the ticket. They've got a pretty good bus transit system, I've used it often. Granted, there are all kinds of people riding the bus, but mostly it's just folks getting to work or students.

At the airport you go to the baggage claim area, then take the stairs or elevator down to ground level (they call it Ground Zero). The buses pickup there. Have some change on you like a few $1 and quarters, the drivers can't give change back, the machine is locked. This trip will take about 1 hour 15 minutes according to the timetable, plus the wait time at bus stop for next bus to arrive, which can be 15 minutes or so. But getting out to the Red Rock and Summerlin area is a good distance even by car, probably would take about 30-45 minutes minimum, depending on traffic on the 215 expressway. I think the Allegiant HQ used to be on Paradise, much closer to airport, then they relocated to nicer area in Summerlin but much farther from airport.

http://www.rtcsnv.com/transit/

LV bus system map:
http://www.rtcsnv.com/wp-content/upl...ap_Oct2014.pdf