Paved road (with optional short trail in one section in Coos Bay & some optional trails in the park itself) and state hwy generally with (poorly maintained) shoulders until past Charleston heading west. Some rises but no real hills.
No fees on a bike.
Pass by Sunset Bay itself, Sunset Bay SP Campground (an awful place to camp on a bike), Shore Acres and Cape Arago SP all in an ~8mi stretch of paved road that ends at Arago. Watch for clueless tourists, but if you take the lane where things are not safe to pass you should be fine.