The cheapest way to get to downtown Seattle would be the Link light rail. It’s $3.25 per adult, free for kids 5 under, and I think 1/2 for kids over 5. You would have to keep your luggage with you, but unless you would be heading downtown during rush hour, there should be plenty of space. The Westin, Sheraton and the Mayflower are all within walking distance from the station with no hills to navigate, so doable with luggage. The Mayflower is very close (on the same block). The Westlake Station is where you would get off downtown. The Westlake area has lots of restaurants, and both Pike’s Place Market and the Monorail to Seattle center are very close by.
If you are looking for the least hassle, I know Seattle Flate Rate Airport Taxi has town car/SUV that will can pick you up in front of baggage claim so you don’t have to take up the elevator and cross the sky bridge to parking garage to get Link rail, or down to shuttle/taxi/Uber areas.
The flat rate, is about $75-80 downtown and $30-40 to the pier the next day. You could also take an Uber from downtown hotel to pier since it’s a pretty short drive and would be cheaper and more flexible if you were going to check out Pike Place market or Seattle Center in the morning.
If you are only planning on being in Seattle for the night, so not planning on doing much the morning before the cruise, you might consider using the cruise line transfer or flat rate to the pier the next morning and just stay in an airport hotel that has an indoor pool for the kids. You’ll have to pick up a shuttle from the parking garage, but might be cheaper.
Because of the pier 91 location, downtown Seattle isn’t really more convenient to get to the ship, it’s just closer, and if you have time, there’s much more to do.
