I have some for the city, but because I spend so much time running around the rest of the state, I've developed a pretty good regional list too. I'll give you my Seattle list first:
Capitol hill is "The Gayborhood"
The Central District is "The Seedy"
First Hill is "Pill Hill"
Puget Consumer's Co-op (PCC) is "The Hippy Dip"
Group Health Cooperative is "Group Death"
Boeing is "The Lazy B"
That freeway that runs through town? It's "I-5." Pronounced "Eye Five." It is most assuredly NOT "The Five" nor is it "The I-5." Just "I-5" thank you. If you can't handle that, go back to California.
Union Bay, near Husky Stadium, on Lake Washington is Garbage Bay to sailors and fishermen. Years ago, it was Seattle's garbage dump. Metro cleaned up Lake Washington a long time ago, but the name is still alive among the nautically inclined. In case you didn't know, Metro was created to clean up toxic Lake Washington, they succeeded, and expanded into transit and other areas. (More on that here: http://www.historylink.org/index.cfm?DisplayPage=output.cfm&File_Id=1353) But boaters still call it "Garbage Bay"
Schools:
Rainier Beach High School is "Beach."
Holy Names Academy is "Holy Dames" (all girls)
O'Dea is "Oh, Gay" (all boys)
Seattle Pacific University is "Spew"
EXTINCT: We used to call SeaTac airport "SeaCrap" but It's come a long way, baby. It's now actually a nice airport, so file that one away in the history section.
EXTINCT: The Seattle Times is "Brand X." So-called by Seattle writer Emmett Watson when he moved to the P-I and wanted to take a jab at his former paper.
Oh, and please, for the love of everything that is holy, it is PIKE PLACE MARKET. May everyone who ever calls it PIKE'S MARKET choke on a salmon bone and die.
Outside of the city, around the state:
To the south, that awful smell in Tacoma is the "Aroma of Tacoma."
To the east, the Crossroads neighborhood of Bellevue is sometimes called "Immigration Station" due to the vast ethnic diversity in the middle of a lily-white town.
Also to the east, skiing at Snoqualmie Pass is "Snow-Crumby" because the snow there is terrible. And Alpental is Alpen-Small, for obvious reasons.
Lake Washington Boulevard on the east side is "The Bully"
Anacortes is an ancient Native American word that means "Waiting for the Ferry."
Yakima is Yaki-vegas.
Ellensburg is Eburg
Bellingham is Bham
Bellingham residents are "Hamsters" (Short for Bellinghhamsters)
Spokane is Spokaloo or Spo-Compton
Pullman is Pullmanastan
Port Angeles is PA
Mt. Rainier is The Mountain
Olympia is OlyWA
Wenatchee is Wet-Snatchee (like a vagina)
Walla Walla is often written "Walla²"
Highway 2, from Everett through Stevens Pass and onto Spokane and points East is "the Hi-Line" (It follows the old Great Northern Railroad of that name to Minneapolis)