Not sure if you've seen this, but there are rules about collecting fossils in WA. In some places, like certain parks, you need a permit.
http://www.dnr.wa.gov/RecreationEducation/Topics/HarvestingCollecting/Pages/fossil_collecting.aspx
I'd guess that eastern Washington may come up with amphibian finds, given what it used to be. It's really hard to say. They have a bunch of maps, but I haven't really heard of caudate fossils found in Washington.
You probably have seen this, but Burke museum has a cute map showing fossil sites.
Cruisin' the Fossil Freeway
I like to keep up on fossil finds since paleontology was my first fossil love, but I haven't found much on amphibians around here.
With a little research looking at these maps:
The Paleontology Portal
You'll probably be able to estimate a little where there might be things, but it would be a hunt. I only find crustacean and fish fossils on accident. I've got quite a few finds, but they're all of fish, crustaceans, or plants.
Maybe you should consider taking some trips down here to Oregon though. There is the John Day fossil bed, which has located some amphibians. You could look at the geography here and compare it to Washington to find spots similar to John Day that would yield some results. I haven't looked up the John Day geography map to find its exact placement, but it should be easy to find out. The most fossils I've heard of with amphibians seem to be from the Mesozoic area, but I'm not by any means an authority.
Amphibians - John Day Fossil Beds National Monument
The Paleontology Portal
The Paleontology Portal
Also consider emailing the Burke museum! Good luck, and I hope you find some cool things. Oregon has a lot of fossil areas, and I think the eastern parts of both states are pretty worthy of some exploring. Just the 2 cents from an inexperienced admirer of paleontologists. Also, consider reading Your Inner Fish if you're interested in caudate fossils. It's super.
