No, however public transit from the airport is very inexpensive.
No shuttle. Had to use Uber
No, but it's cheap to get an Uber to West Lake Center and catch the light rail.
Hotel does not have shuttle. We took Uber because we had lots of luggage.
The hotel itself doesn't have a shuttle to and from the airport, there are however multiple bus stops surrounding the hotel, and public transportation isn't too expensive. So traveling between the hotel and airport won't be a problem.
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