How big is your RV? How many days in the Park? Do you want showers or hookups? Have you decided what you want to see? Depending on how big the RV is going to determine how much you can see. Not sure if you are visiting Lake Quinault or the beaches around Kalaloch, in which case you may want to go by way of Olympia and Aberdeen and come back by way of Port Angeles.
I would recommend you make the southbound journey via Whidbey Island, although that will add another ferry expense at the southern end to get back to the I5. I like Fort Eby for camping, but Deception Pass is also nice. The Mukilteo ferry brings you out right at the Everett Boeing plant, so you can do that tour on your way into Seattle from there. Note that there have been other discussions about seeing Seattle from a campground base and there aren't good options.
I do not recommend this plan. You will not save any money due to the costs of the RV and campground fees, and it is inconvenient to travel on ferries and in parts of Olympic National Park in an RV. Campgrounds in ONP do not take reservations, with the exception of Kalaloch, which is in a remote and inconvenient location. You don't say when you will be traveling. If it is in the summer tourist season, you might have a problem getting reservations. Also, a few roads in ONP are closed to RVs.
Some people really enjoy RV touring. If you are one such person, it may be worth it. If you are doing it to save money, however, thing again.
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