The Arboretum is one of my favorite places in Seattle. The plant zones are extremely well maintained, and each zone has its own distinct feel. It is located so close to Seattle proper, yet while there you feel like you're completely submerged in nature.
One very interesting element to me was Azalea Way, one of the primary paths through the park. It is a wide road paved in well trimmed grass.
Recently completed was the Pacific Connections Garden, which includes a small pavilion. Eventually, this area has the potential to be extremely interesting, but right now it's too new for the young plants to hold any visual interest. It's more fun to visit the more established areas.
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The visitors center has a gift shop, information desk, and bathrooms. They also sell plants. I'm always tempted.