Having lived in both for many years, I'm not sure how anyone could come to the conclusion that nature is more difficult to access in Seattle than the Bay Area. It is a 45 minute drive from the skyscrapers to the Cascade mountains proper; in the Bay Area, it is a 3-hour drive to reach anything comparable. Seattle is bounded on three sides by fresh and salt water in equal measure, similar to San Francisco, with a large boating culture. The city is even nicknamed ("The Emerald City") by virtue of its many expansive and semi-wild parks in the city, plus the general greenery of the surrounding region.

I am a pretty avid nature enthusiast that spends a lot of time in the outdoors. It isn't even close, whether you are looking for mountains, water, or parks. Seattle's reputation in this regard is well-deserved; I'm not sure if there is another metro of its size that is so embedded in and connected to nature. And if you look at map, it is easy to see why -- the city is essentially surrounded by water that is surrounded by very rugged mountains (which has provided challenges for growth).

FWIW, the other large metros in the Pacific Northwest (definitely Vancouver and to a lesser extent Portland) have similarly exceptional access to nature. Some of the Mountain West cities also have great access to nature, though not as diverse as Seattle.