This MacGregor's Plaid Book is published (print and online) for all the local areas around Puget Sound. They are very handy, and free. You can do an online search for "private schools" in the areas you mentioned -- they are all listed in the Skagit Valley directory:
http://skagitvalley.plaidnet.com/
Just a warning about Anacortes but especially Oak Harbor -- you'll be constantly exposed to the unbelievable noise from the Naval Air Station's overhead jets -- low-flying and ear-splitting.
Burlington or Mt. Vernon are on the mainland, Anacortes is on Fidalgo Island, Oak Harbor is on Whidbey Island. Oak Harbor is reasonably priced, Anacortes is very expensive, Burlington and Mt. Vernon are also reasonable.
Shopping and civilized amenities are best on the mainland, all right in Oak Harbor, and not great in Anacortes. Also, Anacortes is a popular retirement place so you'll be amongst an older population.
Hope this helps.