On Google Maps, google "Ancient Lakes". It's NW of George and SW of Quincy. We went there in November. Maybe not a great idea in snake season, whenever that is. Autumn/winter/early spring might be best. Make sure your dog does not bother any wildlife, esp. in nesting season. Start early, make a long day of it, loop from Ancient Lakes over the plateau to the south and come out via Dusty Lake (be prepared for the occasional "corgi toss" in the talus there).
Geologically, a unique and amazing place: flood basalts, channeled scablands. You can see that these lakes are gradually draining; my guess is they were formed when their drainages were dammed by debris from the cataclysmic Missoula Floods down the Columbia channel. Look up "Channeled Scablands" and "Columbia_River_Basalt_Group" on Wikipedia before you go.
Dawgs in Cougar country, look out (I work at U.W.).
Here's a link for a crude road map (you'll need a better one for hiking):
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Gingko State Park, out of Vantage on the west bank, is great desert dogwalking, esp. around April when the desert starts to bloom: