Welcome to the board.
You're trip sounds really fun and I'm sure you'll have a great time. We live in Southern California so if you're in the area we have a spot available for you.
Our daughter-in-law is Austrian and we were lucky to visit Vienna a few years ago. Beautiful city and lovely people. You might look into purchasing a national parks pass for around $80 but it will enable you to get into all national parks and monuments for free. You would still have to pay to camp but if you just want to spend a day it's a good deal.
Someone already mentioned coast highway in California and in fact the coast highway all the way to Canadian border is spectacular. Parks pass will come in handy if you get to Utah make sure you visit Capital Reef, Canyonlands, Arches, Bryce, and Zion parks. The road between Capital Reef and Bryce should not be missed.
Depending on the time of your trip a group of us meet out near Capital Reef in May and again in September. You might also want to check out this web site. www.BMWST.com. Real nice bunch of folks from all over the country.