Washington State:
[ul]
[li]Jimi Hendrix[/li][li]Kurt Cobain[/li][li]Bing Crosby[/li][li]Quincy Jones[/li][/ul]
I’ll go with those two as a start:
Les Paul
Liberace
Steve Miller
Woody Herman
Honorable mention: Al Jarreau, Butch Vig (mostly as a producer), Robin Zander, Bobby Hatfield,
Oregon:
Curtis Salgado, blues master and inspiration for the Blues Brothers
Esperanza Spalding, jazz bassist and singer
Thomas Lauderdale, founder of Pink Martini
Lee Dorsey (born in NOLA, moved to Portland at age ten), Ya-ya, and Working In The Coal Mine
Well, you did say that “there are tons more” that you “could easily have added”.
So if the implied continuation of “could easily have added” is “if this were a different poll asking a different question”, then yeah, I guess you have a point.
mmm
I would certainly allow Mancini. The OP should have clarified that the Mount need not be limited to performers.
(I had to Google Ted Lewis) 
mmm
OHIO
Stiv Bators
Rick Derringer
Trent Reznor
Joe Walsh
What?! How could you have forgotten Gerry Marsden? Or the great Holly Johnson?!
I’m from New York, so this is a tough one, but here are mine:
Paul Simon
Irving Berlin
Ella Fitzgerald
Billy Joel
Ella was born in Virginia, but moved to NY in very early childhood. Sadly, I think adding Bob Dylan would be bending the rules. And John Lennon would be breaking them.
Remove Harry Nilsson and put in Dave Brubeck.
I don’t think Joplin qualifies based on the OP’s ground rules (he moved to Missouri as an adult), so I’ll replace him with Grace Bumbry.
:smack: For some strange reason I thought Berlin was a NY native. In his place, I’ll put in George Gershwin.
New Jersey:
Sinatra
Springsteen
Frankie Valli
Whitney Houston
But this leaves off so many good ones.
Florida:
Ray Charles
Tom Petty
Ronnie Van Zant
Vanilla Ice
I strongly disagree with your last choice (a one-hit-wonder whose career was a total joke). There are dozens of other more successful rappers (Flo Rida, Pitbull, T-Pain), not to mention Jim Morrison and Gloria Estefan.
Build your own mountain. 
Sir, need I remind you that Vanilla Ice was in Teenage Mutant Ninja Turtles II: The Secret of the Ooze?
There you go.
From John Nova Lomax’s Musical Guide to Post-Secession Texas:
If Florida wants to claim him, feel free! We Texans will be busily carving faces into several peaks of the the Davis Mountains. (A part of Texas that is not flat!) Blues, Country, Rock, Tejano… And one peak reserved for The Late Great Doug Sahm–who Played It All. (Hey, I notice one Louisiana list that omitted Clifton Chenier. Since he lived in Houston while he was inventing Zydeco–can we claim him, too?)
Agnetha
Benny
Björn
Anni-Frid
Guess which country?:o
This is a tough code to crack, but I think I’ve got it.
The last letter of each name spells A-N-D-Y, so I’m thinking you live in North Carolina, where The Andy Griffith Show is based.
What do I win??
mmm
Rudy Vallee, Trey Anastasio (and the other members of Phish), and Grace Potter.