Salt Lake sucks in this regard.
There's only two current high school (buildings) that were built pre-war: West and South. West still exists, but South was closed in the 1980s and is now part of Salt Lake Community College, so, it's not even a high school anymore.
Still, it's all we've got:
West High:
South High:
South is a good art deco quality but again, not a high school anymore.
The best, though, was Salt Lake City High School (later changed to East - so, yeah, the three public high schools in the city were named East, South and West). But they demolished it in the 1990s because it was not structurally sound and would not withstand a major earthquake (or so they say). I really wish they had kept it:
It was replaced by the current East High (same location) that is now known as the high school used in Disney's High School Musical:
Not remotely the same - and despite its famousness ... it sucks. Especially compared to the old building.
Highland, built on the city's south-east side, doesn't fit the bill, so I won't include it.
Expanding beyond the city limits, into South Salt Lake, there was Granite High, but that was demolished a few years ago: