Taxi cabs, uber, and lyft.
No but you can use taxi or uber, the airport isn't far.
Approx 25.00 to airport by taxi.
There is no airport shuttle. I recommend using Lyft or Uber because these taxi drivers are desperate these days and try to swindle your rate by tripling it.
As per my knowledge Ceasers Place doesn't have Shuttle service, but the airport is not far and you can easily get a Taxi
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