What are the Seattle NHL teams' rivalries?
Vancouver will be the natural geographical rivals.
Vancouver for logical reasons, will be the main one.
There will be a natural rivalry with Vancouver. It will take time to establish rivalries with other division opponents, and even longer for any in the rest of the Western Conference.
Well the most obvious rivalry would be with Vancouver (a short drive across the border - fans from each team can easily visit the other's arena). It is already being marketed that way (at least here in BC).