Pretty much everywhere between, say, Scandinavia south to Turkey and from there east to India or so. Anywhere, in other words, where you historically find herding peoples who consume the milk of ruminants, be they cattle, yaks, goats, sheep, water buffalo…camels even. Just when and where yogurt first appeared no one knows, but there’s no question that it happened several millennia ago, when humans first began to domesticate animals.
The first fermentation of milk into yogurt was undoubtedly an accident, for just like a bowl of grain slurry or fruit pulp left out at room temperature, milk ferments all by itself without any additional help from people. Opportunistic lactic acid bacteria move in and start disassembling milk sugar molecules (lactose) into simple sugars they can eat. The side effect of this micro pig-out (or one of them, at least), is acid. That acid makes the environment extremely unfriendly to other types of microbes, notably most of the kinds that are dangerous to humans. Which makes it a pretty good deal all the way around.
Another nice thing about fermentation is that in addition to making foods taste good, it preserves them, for days, weeks or even longer. Which would have been a very, very good thing for Eurasian herding peoples living several millennia ago, since Maytag had yet to invent a portable refrigerator light enough to transport on yak back. No wonder yogurts are found in so many places and in so many styles. They just make too much sense.