And the other thing is the Oregon Coast can be driven in a day (two at the most) with a lot of stopping to see things. So if you stayed at a timeshare, you'd have to loop back to it, unless you were staying there for only one or two nights. So in that case, Jim's suggestion would be good. Renting something along the route would be better.
If you mean to use the timeshare as a base camp, then Newport is probably the most centrally-located. You might benefit from reviewing the timeshare map here on Tug.
https://tug2.com/tsmaps/TimeshareMaps.html
If you started at San Francisco, heading north along the closest roads to the Coast, after Point Arena, the next timeshare isn't till you get to Newport Oregon. (Not sure about Gold Beach - I don't think I've ever seen it on an Exchange list.) From Newport, heading north, there are a number of locations, but they aren't that far apart. Seaside, Oregon, is about the furthest north in Oregon. Crossing into Washington, there are a few around Long Beach, Washington, and a couple in the Ocean Shores area. But then you're kind of done. There isn't much north of Ocean Shores
By the numbers, from Newport, Oregon to Long Beach, Washington, is only about 150 miles. From Newport to Crescent City, California (just across the border) is only 230 miles.
If I was going to do it, I'd fly to Portland, Oregon, rent a car and head to Astoria, Oregon. Drive down the Coast, stopping at will, until you get to Eureka, California. Then you can head slightly in land, and end up in San Francisco. Lots to see that way, and easy driving, if you're not in a hurry. And there are many, many, MANY motels along the way.
If you're coming here in October or November, be ready for cooler, wet weather. Fall storms usually start in October, and it can be pretty grey along the coast. Things are often fogged in. You might want to wait six months, and come in May instead. Weather may still be rainy, but there is a better chance for sunshine, and the weather will be generally nicer than in the Fall.
Dave