Melaleuca in Golden Gate Park (sketch by Heath Massey)
Next to the Ghiradelli Rustic Shelter, a hang-out for chess and checker players just north-west of the Conservatory of Flowers in Golden Gate Park, the serpentine trunks of an old (possibly dying?) Melaleuca tree must be an irresistible jungle gym for children. Going by the needle-like leaves and the bottle-brush-like, white flowers, I tentatively identify it as Melaleuca armillaris (Drooping or Bracelet Melaleuca), although I could be wrong. This species is discussed in Elizabeth McClintock’s Trees of Golden Gate Park, and she pinpoints one in the Botanical Garden that is still there and looks similar. But, as McClintock points out, there are more than 100 species of Melaleuca, most native to Australia and quite a few of them have been introduced in California. The interesting bark of this tree is not as shaggy as is typical; in fact the undulating coils are worn shiny in some places, like the wooden bannisters in old houses after years of hand polishing.
It’s hard to know how old this particular tree is, but according to McClintock this species of Melaleuca was stocked by at least one California nursery as early as 1854 and many were available in California by 1871. So this could be one of the older park trees. The one in the Botanical Garden likely dates to the 1940s, when the earliest Australian plants were introduced there. But by my distinctly unscientific estimate, this one seems more wizened and time-worn; such depth of character takes a long time to develop. Think of all the chess games it must have silently witnessed.
golden gate park: views from the thicket 
Did you consider Leptosptermum (tea tree) for your identification? It is also common in GG Park. Here’s a link to the GG Park botanical garden description of it: http://www.sfbotanicalgarden.org/garden/bloom_08_04.shtml. Leptospermum also sprawls on the ground in a very attractive way, getting more sculptural as it ages. I had one for about 20 years and it just kept getting more and more interesting until it died suddenly and inexplicably It was a terrible loss in my San Francisco garden.
Yes, Leptospermum (Tea Tree) is another gorgeous Australian import with sculptural trunks when older, but I’m pretty sure the one I drew is Melaleuca armillaris. It looks just like the one in the botanical garden next to the duck pond near the Friend Gate. The white bottle-brush flowers are a give-away, different from Leptospermum flowers. Sorry about your loss of that beauty in your garden, though.