A local blogger has some great posts dedicated to Paleo-friendly restaurants in Seattle which I've found useful:

http://whatsinwhatyoueat.org/category/paleo-in-seattle/

I live in the Tacoma-area but here's some I've visited/heard of that seem to be somewhat paleo. Obviously not the ideal solution (no grass-fed meat that I'm of, probably grilled/fried in corn oil, etc.) but you get the idea.

The Counter (http://www.thecounterburger.com/seattle/): Get beef, lamb, chicken burger in a bowl with veggies

Ipanema Grill (http://www.ipanemabraziliangrill.us/): Never been here (it's a bit pricey) but lots o' meat

I would assume many of the sushi restaurants in Seattle would be pretty Paleo if you stick to sashimi and veggies (no rice, sake)

You can always pick up some food from Whole Foods/PCC Natural Markets (a few locations in Seattle) if worse comes to worst.

Results from Yelp for "Paleo":

http://www.yelp.com/search?find_desc=paleo&ns=1&find_loc=seattle+wa

There's also Thrive near Roosevelt Whole Foods, and while they're gluten-free, they're also vegetarian which means no meat. http://generationthrive.com/

Ipanema Brazilian Grill (206) 462-3317 1225 1st Ave (Seneca Street) Seattle, WA 98101

It's $40 prix-fixe. Yes, it's expensive. To really get your full value avoid the grazing bar full of filler food and go straight for the meat. The lamb, especially, try to get there before the rush so you get all the crusty crispy om nom nom fat on the outsides of all the cuts. If you've ever been to a Fogo de Chão it's pretty much the same deal, except it's cheaper.

I have the same question for lunch spots in downtown seattle. Here are my experiences so far...

Ipanema is great for lunch, and much more reasonable than the dinner price if you have time to sit down. As always, Chipotle is a good option for lunch. the Market Fresh Salad bar is ok. I also like the curry salad at cafe Zum Zum.

I seriously enjoyed Lola and Palace Kitchen.

I live in Seattle (Queen Anne) and there are some great options:

Emmer and Rye in Queen Anne (their menu is online) -- any time potatoes are on the menu, I just ask for extra green veggies and they have no issue with it. Also, you can either email the chef directly or just ask the wait staff about the ingredients and if sugar is in the dish. I go here a lot and love it.

1-2-3 Thai in North Queen Anne -- just order extra salad (without dressing) instead of the rice, and many of their dishes are Paleo-friendly (the basil chicken is outstanding). It's cheap and super-quick.

Rhodies Smokin' BBQ in Belltown (across from Space Needle) -- it's the best BBQ in Seattle and it's in a small take-out place by a gas station! The portions are huge, the prices are low, and their food doesn't come covered in sauce (just tell him -- no sauce). They offer a low-carb cole slaw as a side (just get double cole slaw and not the beans).

Sinbad Express in Fremont -- it's very cheap, and very fast. I've only eaten their once and I had a lamb gyro salad. It was tasty.

Madhu Cuisine of India in Belltown -- they have a good and (mostly) Paleo-friendly lunch buffet, plus they have a good size tandoori platter. Cheap, too.

Get the Porterhouse at Jaks...order veggies instead of the starch. Serious yum.