My DH and I have cruised a total of four times on Celebrity, three on Princess, and three on Royal Caribbean. We chose Celebrity because we love the service and the small touches that make them stand out above other cruise lines and because they offer in-cabin babysitting at night (when our kids are sleeping).
We flew into Seattle two days early. Our 35 month old DS used a Cares harness on the plane to keep him still and in his seat. We took turns holding our 15 month old DD. We did not take our carseats because we had so much luggage. We took the Downtown Airporter bus to the Sheraton Downtown. This is a very nice hotel and the location is very convenient. I booked it on priceline. From the hotel to the pier we took a ten passenger van and we took the cruise line bus back to the airport. If you can take a taxi by all means take the taxi. The cruise ship buses let you off 100 yards or more from the airport and there were not any porters to help with our luggage. On the ship, you can pay $20 a person to have the ship take care of your luggage by checking it from the ship directly to the plane but our airline (Midwest) didn't participate.
In Seattle we went to the aquarium while my parents did the Underground tour. My parents enjoyed the Underground and we had fun at the aquarium. The next day we went to the zoo. The zoo was wonderful but we only saw 2/3 of it before heading to the Space Needle. We took the public bus from downtown to the zoo and then on the way back the driver let us off at the closest stop to the Space Needle. We took the monorail back downtown.