The Lookout on the Palisades is over 17 miles, as the eagle flies, to the Empire State Building. The Marin Headlands are under 6 miles, as the eagle flies, to the Transamerica Pyramid. So technically the Marin Headlands are much closer to the urban core.
Not only that, the Palisades are but a tiny sliver of land, with what appears to be a lot of trees, yes... but not much else. The Headlands are just a small fraction of the Golden Gate National Recreation Area, which then flows seamlessly into Muir Woods, Stinson Beach, Mt Tamalpais, and the Point Reyes National Seashore. Basically
40 miles(!) of untouched, continuously publicly accessible open space,
5 miles from the urban core.
The diversity of the landscape is also quite profound, not only with the micro climates but the flora and vegetation. It's not just "dry dust". There are drier woodlands and chaparral shrubby areas and coastal praries, but also fog bathed coniferous forests with coastal redwoods and Douglas fir, wet meadows, waterfalls, creeks, and marshes. All this punctuated by sheer cliffs plummeting straight into the Pacific Ocean.
Let's be honest. NY has the concrete jungle thing on lock, but when it comes to preserving open space that is readily accessible from the urban core, SF takes the cake easily. Not only do you have the Marin Headlands, but to the south, you've got the same spectacular coastline stretching down to Half Moon Bay, Santa Cruz, and beyond.