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JKR doesn't ever specifically says where it is, but I think it's generally believed to be Russia, Germany, Bulgaria (since Krum played for their national Quidditch team), or one of the former Soviet republics.

But, I don't know about the headmaster at all. I don't think she mentions it in HBP. I'm sure someone will be along to correct me if she did! LOL! I remember Krum implying that Karkaroff (sp?) was a pretty weak headmaster. While I was searching around for any info I could find about Durmstrang getting a new headmaster I found this quote from Draco on a message board:

"...Father actually considered sending me to Durmstrang rather than Hogwarts, you know. He knows the headmaster, you see. Well, you know his opinion of Dumbledore - the man's such a Mudblood-lover - and Durmstrang doesn't admit that sort of riffraff. But Mother didn't like the idea of me going to school so far away. Father says Durmstrang takes a far more sensible line than Hogwarts about the Dark Arts. Durmstrang students actually learn them, not just the defense rubbish we do ..." POA, UK edition, page 163

Well, Krum took that Hermione to the ball, so I guess they do admit that kind of riffraff after all. But, it's interesting that Narcissa didn't want Draco to go to Durmstrang.