I have been doing pilates for about 15 years. It has saved my physical body, from slips or falls. I do private lessons.
While you requested West Seattle, my pilates instructor is in Burien and works out of her house, she has a beautiful studio. She has just expanded it.
She is a former classical dancer, and has been teaching pilates about 15 years or so.
Here is her website
http://www.newlifepilates.com/.
Her prices are very reasonable too.