Another problem you will run into when trying to use a small airport such as ALW or PUW is that some partners don't recognize it and don't publish fares from there. I ran into this problem when JAL would publish a ~$800 fare on GEG-TYO, but trying to price it out of PUW would result in a broken fare that was ~$8000+ in economy.

Basically the decision for me came down to the consequence if I missed the connecting flight.
Going to LAX? I would fly from PUW - there are lots of SEA-LAX flights.
Going to PEK? I would fly from GEG - not going to risk missing the once-daily flight.
NYC/WAS? Probably PUW, unless the connection time was absurdly long.