Full disclosure: I live here and am a bit biased. However, I have lived in Seattle for 30 years and know the city well. If you are visiting from out of town and want to get a taste of Seattle culture, this is a place to do it.
The best area right now in Capitol Hill is the "Pike/Pine Corridor". It is basically the area from downtown up to 12th Ave on both Pike and Pine. Some of the best restaurants/bars in the city are here. Oddfellows, Po Dog, Barrio, Quinns, Honey Hole, Sun Liquor... can go on and on.
Plus you have the last great independent bookstore in the city; Elliot Bay Books.
This is definitely the heart of Seattle culture as well as the gay area of Seattle. Don't be scared away if you are straight, however. This area is definitely main stream. For the best in gay Seattle, check out Purr, Lobby, Q, Pony; all within the Pike/Pine area.