Paul, you've already gotten some good advice here and I'd echo most of it. IMHO, if you're looking for an experience most resembling what you found in Healdsburg - an attractive town with walkable wine tasting and dining choices, in WA/OR, you're most likely to find that in Walla Walla. As has already been pointed out, though, WW is a half day's drive from either of your likely airports (Portland or Seattle). If you'd like to minimize time in the car, then you may prefer flying to Portland and sticking with the Willamette Valley. Weather there in the summer would be cooler than in WW but also relatively more humid. Think a slightly warmer version of the south of England and you wouldn't be too far off. As Bruce warned, WW can be very warm, with mid-summer average high temps in the low 90's (F, of course) and 100 not that rare. On the other hand, as Bruce also said, it is quite dry and so perhaps not as uncomfortable as those numbers might imply. Still, lodging that offers a swimming pool might not be a bad idea

Woodinville is a bit of an oddity. It hosts a fair number of quality wineries and so if tasting is the main object, may be worth a visit. If it's a wine country experience you're looking for, not so much. It's an ex-rural place in the process of morphing into suburban Seattle/Bellevue where marketeers seem to have chosen the winery locations - close to the customers but not to the grapes, almost all of which come from several hours' drive away, east of the Cascades.
If you're having a hard time making up your mind, let me suggest another tie-breaker: do you have any strong preferences on varietals? In the Willamette Valley, Pinot Noir is the predominant red (so much so, whatever's second rates barely an asterisk); Pinot Gris and Chardonnay are the main whites, probably followed by Riesling. In Eastern Washington (where WW is) you tend to get grape varieties that require more heat to ripen. Historically but increasingly rarely there was Lemberger/Blaufränkisch; Cabernet and Merlot dominate in terms of plantings but more recently the trend has been towards the Rhones (Syrah, in particular). For whites, the ubiquitous Chardonnay is still king and there is a lot of Riesling planted but again the Rhones (primarily Viognier) are on the rise. Of course this list isn't exhaustive and you'd find other varietals in both places but if you have strong preferences, you might let that help guide your choice.