Two places I'd go are, unfortunately at opposite ends of the state. First, Walla Walla. Stay at the Whitman Hotel. It's a small downtown core, and there are many tasting rooms within walking distance, and several great wineries close by to drive to.
Second, there is nothing worthwhile in downtown Seattle anymore. I work there, and I no longer recommend it for tourists. For winos, you want to stay just outside Seattle in Woodinville. preferably at Willow's Lodge. There are over 100 wineries and winery tasting rooms in Woodinville, mostly clumped together in a few industrial parks, which makes to visit several in one location. Here is some info: https://woodinvillewinecountry.com/