Not sure what my climate zone is, but it's San Jose, California--dry,
summers get to 90-100 on hot days, winters have occasional freezes but
usually only once or twice a season. Lots of sun.

Right, and less rain than other nearby areas (the usual climate zones
are just about the coldest winter temperature - they don't express how
hot and dry San Jose summers are, even compared with San Francisco,
Santa Cruz, etc). So forget about coastal redwood for example (well,
it is probably too big as well, but the point is that it won't be
particularly happy about the San Jose dry climate).

Maybe California Buckthron (
http://en.wikipedia.org/wiki/Rhamnus_californica )? Maybe too short.
That page says "2-5 m tall" (6-15 feet) and I don't know if 15 feet is
as big as you want even if your plant did get that tall.

Madrone has beautiful bark (
http://www.calfloranursery.com/pages..._a/arbmen.html ).

I don't know, I didn't have a garden when I lived in California. So I
don't really know these plants from a gardener's point of view. I'm
mostly just browsing sites like:

http://www.baynatives.com/
http://www.berkeleyhort.com/gardensu...a07_trees.html
http://www.calfloranursery.com/pages...sts/trees.html

I would spend some time researching what to plant. Even a
fast-growing tree will probably take a while (and the fast-growing
ones may have other problems like short life). Picking the right tree
will increase the chances that it survives, lasts a while and does
what you hope it will.

You might think about trying out a few non-trees (maybe just while you
are waiting for the tree to grow up). Something like a vine on a
trellis/cage, or some taller flower like a goldenrod, might partially
block your view of that neighbor's shed while you wait for the tree to
grow up.