When the last Burdines sign came down a few months ago, more than just a trademark disappeared from the Miami landscape; a homegrown and nationally admired institution faded into the Magic City sunset. Burdines began as a little outpost selling its wares to railroad workers, soldiers headed to war in Cuba, and a small but ethnically diverse population. Both city and store grew rapidly in the tropical warmth. As Miami became a world-class tourist destination, Burdines grew to cater to visitors as well. By the Thirties, the company began producing its own line of clothing that became the rage in colder climes. Those ice freaks, it seems, wanted a little imported sunshine.