You don't want midway, either the airport or downtown. Downtown can be double the cost of airport locations.
Some points to consider, what time are you getting to Seattle and what do you want to do when there?? Then pick a location that allows this. If you have a later day arrival, your cheapest option would be to stay near the airport, then cab to the ship, drop off bags and sightsee Seattle until later afternoon. REAL easy to do if sailing NCL since they use the downtown Pier 66 dock- just walk to Pike Market.