...is really more a gently falling mist. Most of the time. Growing up in the Pacific Northwest I was always confused by the concepts of "raincoat" and "umbrella".
Any reasonably water-resistant coat will keep you comfortable. Even a tight wool fabric will be fine - hence the flannels of the 1990s. Wear layers, as it could be 40 degrees or 80 degrees in early June, and one of those layers should probably involve a hood.
Besides, you'll be popping in and out of restaurants/shops/museums. The only time you really need to *worry* about being wet is if you're hiking -> can't stay warm -> risk of hypothermia.
Mind you, Murphy's Law now says that you'll get torrential rain for days when you visit. In that case, pick up a cheap umbrella when you arrive.