Are you looking for something specific?
If so, here's the best strategy.
1. The first good place to try would be the Washington State Liquor Control Board. Here in Washington, all hard alcohol is sold through state owned and operated stores only. Weirdly enough, though, they also sell wine; even more strange is their pricing policy. Everything is sold at a fixed markup; as a result, some wines are relatively cheap at a [depressing, inconveniently located] package store near you. Do use their search engine to see if they have what you want, and where it's in stock. Eroica brand riesling, for example, is $15.99 at state stores, but $19.99 or more elsewhere.
2. If they don't have it, it's time to do some online shopping. The only sites that are IMHO consistently worth your time are K&L, The Southern Hemisphere Wine Center, and The Wine Exchange. Everything else is pretty much noise. Remember, it costs about $2 a bottle to ship stuff to Washington, so it doesn't make sense to buy wine cheaper than $24 online unless there's no other way to get it locally. This is often the case, and yeah, it can be cheaper to just have it shipped than to drive into town, pay for parking, and pick it up in person. I'm lucky in that the UPS office is on my way home for work, so it's not a detour to pick up my wine on the way home. [As you might expect, the UPS counter agent knows me by name at this point - it's pretty funny. Or is it embarassing? I'm not sure...]
3. If those sites don't have it, try http://www.winesearcher.com. This site is very helpful if there's something obscure you just can't find at the usual Web shops. Caveat emptor, though: a lot of the shops that are linked to this site strike me as pretty dodgy. Still, you never know what you'll find: I once found a bottle of 1999 Clonakilla shiraz viognier for $29 from a shop in San Diego desperate to get rid of it.
4. Finally, if you can't find it online, or if it costs less than $20, it's time to go local...
Obviously, this isn't a complete list of all the wine shops in Seattle, but these are the only ones that strike me as being really good. Here are some quick notes on what they're like:
Seattle Wine Co. is superficially the least impressive of all of them. It's in a strip mall just around the corner from an Arco station - it doesn't look promising from the outside. Inside, it's terrifically bland, with nothing but stacks and stacks of wine. Thing is, though, the guy that runs it has excellent taste, and he isn't wasting your money on fancy displays or signage. Yeah, handwritten signs thumbtacked above stacks of cases are kinda low rent, but when you can buy fabulous wine more cheaply than anywhere else, who cares? He's also more than willing to do special orders, and is chatty [but in a pleasant way]. Their selection is a great mix of cool stuff from all over the world; he carries both kick ass $8 wine as well as some seriously pricey bottles [like the $40 bottle of Spinifex I picked up this afternoon]. Recommended.
If you're in a spendy mood, they have a 7-pack for $350 that's amazing value: 2x Col Solare, 2x Northstar merlot, 2x Conn Creek Anthology, and 1 bottle of the Dr. Loosen-Ch. Ste. Michelle Single Berry Select riesling. I was tempted... but that's out of my price range.
Pete's looks more like a 7-11 than a wine shop, but again: do you really want to pay for chic wooden shelving? No? Then you're cool. Their spartan Web page has got a monthly sale list, but otherwise virtually no info; even more annoying is that no mapping software can find their Bellevue store [it's mapped up there - it's near Chahtanee Thai restaurant if you're trying to find it]. Inside, it's like a dim, dodgy minimart with battered shopping carts - but again, good pricing and a stunning selection of Pacific Northwest wines. Interestingly enough, they also have incredibly cheap beer and San Pellegrino soda. Generally speaking, the sale wines are your best bet, but it's definitely worth checking out the rest of the store just for the hell of it. Their Australian wine buyer is pretty good too, although it's usually cheaper to mail order anything more expensive than $20.
The Costco in Issaquah is notable because it's also where the company's headquarters are. As a result, they often have weird, small lot stuff they maybe bought a few cases of just to try it out - and of course they have all the usual Costco standbys like super cheap party wine. If you have a Costco membership, it's fun to check it out from time to time. Right now, they've got cheap Penfolds Bin 389, for example.
Esquin is the "fanciest" wine store in Seattle, or at least the wine store with the best balance between reasonable cost and super high end stuff. There's something about the place I don't really like, though, but don't let that put you off. Their Web site also has monthly specials, some of which are good deals. Still, once you get in there, you seem to get stuck in a world frequented more by People With Money than anyone else. The staff is friendly enough, but they seem programmed to sell you something expensively French rather than figuring out what exactly would suit you best. It's telling that I've spent less than $100 there in the two years I've lived here.
Pike and Western is tiny, but cool. It's smack dab in the middle of the tourist hell that is the Pike Place Market. Consequently, parking's impossible, so go on a weekday afternoon. They don't carry a lot of different wines, but what they do is both very well priced and usually exquisite. Plus, they seem to have the killer connections that result in very, very hard to find stuff showing up on their shelves. We stopped by this afternoon to pick up a bottle of Malbec advertised on their Web site, and wound up with a bottle of the 2002 Giaconda Warner Vineyard shiraz. Let's just say that it was, um, expensive. We paid $76. However, bear in mind that  this wine is so incredibly rare that I have never, not even once, seen a single bottle of it for sale anywhere in the world, ever, and  the price of this wine if ordered direct from the vineyard [and mind you, you couldn't actually do that without being on their mailing list, which has been closed for ages] was US $56 upon release. I know $76 sounds outrageously expensive, but all things considered, it's cheap; most wine shops would price that at $140 just because it's so rare. Don't worry, though, they also have really good inexpensive stuff; this was where my first bottle of Susana Balbo Torrontés came from, and that was a relevation at the time - and only $10. Do check it out.
Seattle Cellars has been around for a while now, but I never went there until today. Staffed by exasperatingly perky sales slash fembots, they do have a lovely selection of wine, beautifully presented, at prices that are frankly kinda on the "ouch" side - K&L sells Torbreck 'The Steading' for $23.95, but they wanted $34.95 for the same bottle. Hm. Still, their selection was unique in Seattle, and if you buy by the case, the pricing's a little better with the case discount. Right now, they have a kick ass selection of rosé wines; I wanted to buy more, but I'm out of budget for the month after the Giaconda and the Spinifex. So there.
Finally, although they're not on the map, there are a few wineries in the area, but you probably wouldn't want to go there to buy wine. They're overpriced as hell, and have the nerve to charge to taste almost anything at all. Still, I need to get up to the Columbia Winery someday to ask where the hell I can find their South Church Block shiraz, which is apparently Washington's finest shiraz viognier... one of these days...