"How I wish I could do that..."
I'm gonna let you in on a secret: You (almost certainly) can! It costs less than living in a house, if you set out to live cheaply and travel slowly (the driving part, and the paying nightly rates rather than weekly or monthly rates in RV parks is how you can spend a lot living in an RV). Mobile internet coverage is better and faster than ever, though much more expensive than ever (I pay nearly $300/month). If you're a software developer of any sort, you've got a lot more freedom to live however you want than most people who have ever existed in history.
In theory, yes, but I'm married and have a kid. No way I'd be able to make the lifestyle change. Hence, you're my hero, living the life that I can't :)
Lake Quinault is also really wonderful, and apparently where the term "rain forest" was coined (by FDR, in the version I heard.)
If you're athletic, the climb up Mount Townsend is well worth it, and the trail is really pretty good.
If you like to camp, drive out by La Push and hike a mile or two north from Mora. Hole in the Wall is very interesting. Be wary of bears there, though. Hang your bacon high in the tree.
Mount Baker has lots to offer and doesn't get as much traffic as Rainier.
If you like it dry, there's a great campground above Twisp (northwest IIRC) that is really nice.
For a specific recommendation, there's a lot of beautiful scenery and generally pretty few people along Hwy 20. Once you get off the road, there are many beautiful creeks and lakes surrounded by miles of trails, and not that many people, especially early and late in the season (the highway is closed for winter, and reopens once the snow melts and avalanche danger is back to normal). Check out the area around Stehekin in particular.
Also, you live in an RV - you're my hero! How I wish I could do that...