I'm assuming you're at JBLM.
There are several public airports nearby:
Tacoma Narrows, Auburn, Thun Field, all come to mind.
Plus several privately-owned airports & airparks.
You might try to contact the owner of Port Orchard airport 4WA9.
http://airnav.com/airport/4WA9It's located SE of Bremerton, on Sydney Road, and is a very quiet place.
There are two hangar buildings, maybe totaling 20 hangars,
dunno how many (if any) still have airplanes in them
or how many might be empty & available.
But might be worth looking into.