Geoff,
A good option for parking the land whale is South Beach State Park on the south end of Newport.
http://cms.oregon.gov/OPRD/PARKS/Pages/reserve.aspx
This link will allow you to make an online reservation for an RV site, for $27 you get water/electricity included, and the usual state park amenities in the campground, like showers. I just checked availability for Aug 27 and there are many still open, you could also check Beverly Beach State Park, which is north of Newport. Both have access to the beach.
You need to reserve right away since you are so close in time, they don't accept reservations once you get within a day or 2, and it's high season here. I live in Lincoln City, about 30 mins. north of Newport, glad to see you are making time to enjoy the central coast. I listen to the podcast regularly as I try to move my "urban farm" in a permaculture direction. Welcome to Oregon and the coast!
Joanne