I agree with Matt's in the Market. I often travel to Seattle (6-7 times per year) for work and usually dine solo in the evenings. I had a fantastic dinner there about 2 months ago. I sat at the bar and watched the sun set on Puget Sound while enjoying perfect lamb chops and an outstanding glass of Zinfandel. A treat for all of the senses!
I've also eaten at Flying Fish and liked it a lot, although the atmosphere is a little more Lettuce Entertain You. But it's been a couple of years since dining there so I don't have a lot of specifics to offer.
Another place, depending on where you are located, is Moxie. If memory serves it is run by a chef whose alma mater is Matt's. It's in Lower Queen Anne and offers some excellent dishes and cocktails, although it lacks the ambiance of Matt's. I also like it because it's walking distance from my usual hotel.

Good luck!