My top choice would be Cape Lookout State Park southwest of Tillamook for the best camping experience. The campground is right next to the beach and there are several miles of hiking trails including one to the end of the cape through old-growth Sitka Spruce rainforest. Bikes are not allowed on State Park trails, so you would have to look at other options for off-road biking. An alternative would be Nehalem Bay State State Park near Manzanita that borders both bay and ocean. There are campground biking trails that are more for family recreation, so if you are looking for more off-road biking, you could look at logging roads on Neahkahnie Mountain about 10 minutes to the north in Oswald West State Park. The hiking trails in Oswald West State Park are great, but again, are not open to bikes.

Happy exploring!