None of the downtown properties have shuttles. Super Shuttle has a counter at the airport. There are a couple of local options as well. It will be around $50 roundtrip which compares favorably to taxi fare which is $50 each way.
The Renn has a shuttle but its no where near downtown and there is no easy way to get downtown from there using public transportation.
Alternatively, if you're really looking to travel cheap, the local transit district operates Skyride which runs to major transit stops. One of them runs downtown, a few blocks from the downtown properties. I think the fair is $7-8 each way.