Even though it is the capital of Washington, Olympia is a fairly small town with its 40,000 inhabitants, especially compared to Seattle. It's a very hippy place, and the people are incredibly friendly. Walk down any road with a hitching sign, and you're most likely to get a ride, at least to the highway. Carry around a musical instrument, and you'll get invited to parties. Definitely stop by here if you can!
July 2017: We got stuck in Olympia after getting a ride from Seattle when were were headed towards Portland. They left us in the sourthern part of the city in Tumbwater and it was an absolutely terrible spot to hitch south due to how the road is designed. So I'd suggest going somewhere else in the city to go south. :) basically there was nowhere for cars to pull over. We ended up finding a ride on Craigslist for 9 dollars.