Captitol Forest may not be a bad the next couple days if we get some snow. In Thurston county I think it will be kinda hit and miss success wise but, pretty much anywhere has them. Its more a matter of turning them up, if there are deer or deer cover there is likely rabbits. Like most hunting snow is a great equalizer, otherwise there is usually alot of luck involved. Old field edges next to thicker timber and blackberries always hold sign. Abandoned homesteads and orchards have been my best producers for cottontails. I havent had much success finding a real population of 'shoes in Thurston county.
Personally I would look higher, for "real" hunting. I have had luck in Toutle and Margaret high country chasing 'shoes. If you can find some ground up higher above 2000 - 2500 feet you should have much more luck finding 'shoes. And with the weather we have had it should be good hunting up there as well. Not sure of specific areas in Pierce county, but anywhere up higher with a good combo of mountain alder mixed with noble or hemlock have usually produced. If you dont have snowshoes I would consider them, and also a weapon for predators as odds of seeing a dog or bobcat are decent as well.