Is there a shuttle from the Seattle airport to the Grand Sheraton in Seattle?

There is light rail to Westlake, then 3 block walk. Also, Uber.

Light Rail to Westlake is very convenient and just $3 per trip, then it's just a 5 minute easy walk to the hotel.

No shuttle but there are a few transportation services. The hotel is about 20 min away. Assuming you are arriving in Tacoma international

Unfortunately no