Most of the replies were of pretty spendy restaurants, which is of course fine. You'd be hard-pressed to find a more classic red meat-eating experience than The Metropolitan Grill, or the $40 Argentinian steak buffet at Ipanema (Ipanema Brazilian Grill 1225 First Avenue), or the goat dishes at Sitka & Spruce. These are lovely.
But I'm way more fond of the divey food experiences to be found at the out-of-the-way holes-in-the-walls; places my dad likes to call "gems". Like the succulent Chinese bbq pork or duck at Kau Kau BBQ in the International District (the "ID". Just look for the ducks hanging in the window). Or the cheap but tasty chicken and ginger congee (a Chinese rice soup) at Hong Kong Noodle House on 12th.
I also like the piled high hot pastrami at Market House Corned Beef downtown, the cheap, GIANT and fantastic burritos at Gordito's at 85th & Greenwood just north of Seattle. I'm also impressed by the fish & chips at Jack's Fish Spot in The Market.
Food for regular foodies...
Well this isn't a restaurant unless you bring a bbq grill along, but you can't do any better for a butcher shop in Pt Orchard than Farmer George's. Along with locally raised beef, lamb, poultry & pork, they've got this amazing nitrate-free smoked bacon called Cottage Bacon, mmmm. They also stock wild game & exotic meats. I like getting the locally produced eggs & dairy except that they sell out too fast.
I've been known to drive an hour & a half from Seattle just to get their steaks...