If not mentioned already, the Olympic peninsula has a lot of various hiking trails.
Specifically, what I'm thinking is the
Lake Cushman area; There's Big Creek CG (USFS) that has it's own trail 1.5 mile loop trail along perimeter of CG, but also has a trail head that connects to longer more challenging trails and trail heads (Mt. Rose trail/trail-head and Mt. Elnor trails). Just 3mi (or so) down the road is Staircase CG (NPS) that has has a few trails and trail loops of varying distances as well as that "Staircase" attraction itself.
EDIT: (I read the comments
again) I'd vote for the Olympic peninsula, it'd be easier on the wallet. And since you're not from here, the Olympic peninsula would still be just as new of an experience for you.
You're already mobile, so you could pick up and go somewhere else if you wanted/needed much easier. Someday I'd like to go over and see the San Juan's, but I keep going camping over on the Oly-Pen..... just seems easier and more accessible
(but then again, I'm cheap and introverted)
Good luck to ya, my wife had to go the same journey a couple years ago (
I'm so glad & grateful to still have her with me....
but damn I miss boobs)