I live in eastern skagit county and I can tell you that anywhere on the westside of the mountain range is going to be pretty wet this time of year. Temps are starting to get into the 50's and sometimes high 40's at night.
Personally, if I were you, I would take the highway 2 route through index, gold bar, etc. Such pretty country out that way and there are tons of great places to camp along the river system there in the woods away from people. As long as you have good rain protection, warm clothes, and a decent sleeping bag....that's the route I'd take. Altho, there'll be less rain on the eastside of the cascades so you might choose to take a different route.
Leavenworth is a Bavarian themed town that gets lots of tourists. So it seems it would be a good place to busk/panhandle and make some money. Chelan is full of rich yuppie people that go there for all the shishi wineries they have in the area. Not my cup of tea. But, again, it might be good to make money there if the cops don't run you off (I don't know as I've never tried there). There is a boatride you can take to the little town of Stehekin (a town you can only get to by boat as there is no road system). I haven't been to it but I heard it's pretty and I think lots of people go there to start off on their hikes (The pacific crest trail passes near there).
Once you get to Pateros you can take the side road off to the west (highway 153) that takes you through the Methow valley and to Twisp. Also very pretty country and lots of cool places to explore along the river that winds alongside the road. Just watch out for coyotes and rattlesnakes and don't trespass on anyone's land or ya might shot. Check before you make campfires wherever you are (but ESPECIALLY on the eastside where it's super dry) that they don't have any burn bans so you don't get in trouble.
Lots of rockhounding around Twisp and the surrounding areas and if you get the hankering for a good steak, Thompson's Custom Meats has some pretty good meats. Since you'll be in Twisp, might as well go on and check out the nearby cute town of Winthrop, altho it's mostly little artsy shops along the boardwalk that are catered towards tourists.
Either way, whichever route you decide to take to get there....definitely don't pass up the opportunity to drive across either Stevenson Pass or North Cascades Highway (Highway 20) on your way back. Man, the fuckin views are incredible!!! Enjoy!
North Cascades Highway (Highway 20)
(Ross Lake overlook on Highway 20 - near my neck of the woods)
