Earth N Sky,
As another easterner (Raleigh, NC), I share your excitement about climbing Rainier. Me and a buddy are headed out in July for an expedition skills course on Rainier, so maybe we will see you on the summit.
Having spent a lot of time out there, I agree with the advice not to try to fit the Olympic peninsula into your trip, because it is so massive and time-consuming to get there, you really want to do it on a dedicated trip rather than an afterthought. For future reference, though, you need to go back and spend 2-3 days doing the Hoh River Trail, with or without a climb to the top of Mount Olympus. The trail through the rainforest is really the highlight, and it has the distance you crave. For a good trip report, see "Mt Olympus-Blue Gl in a day" trip report from July 2006 in the Olympic forum on this site. Those guys did it in a day, which is totally sick, especially when the river trail is so beautiful in the daytime. I say 1-day in, 1-day summit and back, 1-day out. For those of us from the east, you just need to spend some time in the awesome wilds out there. You can get more beta on the Olympic forum, but make this part of your plan for another trip.
Have a great time on Rainier and I hope to see you in July.
Chris