Another American who says it “Ed’n’burra”. I got this pronunciation from my wife, who grew up in California but spent several summers in Scotland.
Having been born here and lived most of my life here, I’ll vote for Ed’n’burra as well…
I sometimes pronounce it ‘Ed’n’burra’ but only because my home town ends in ‘borough’ and I forget Edinburgh is spelt differently. When I think about it I pronounce it ‘Ed’n’bruh’ though.
UK, not Scotland.
Here is how one pronounces it if one is from Kirkwall, in Orkney.
Canadian. I don’t live far from Sunspace (and lived in Peterborough for a while). Scarborough’s a part of Toronto, Peterborough’s about 2 hours away.
Ed’nbrra
I’m English but I’ve lived in Edinburgh seven years now.
Midwesterner and my first instinct was Ed-in-berg. Then I remembered, “This is one of those names that doesn’t sound like its spelled just like Monty Python’s Throat Warbler Mangrove complained about!”
Once I remembered, I came close, but for some reason I thought it was a long E, eed-in-burra.
I notice a number of people say “Edinburra” - but isn’t that the same as “Edinbruh” if you put any sort of roll on the R?
And how about “Edinberg”? I remember the doorman of the House of Representatives introducing the Duke (no, not John Wayne) that way once.
I thought I clarified a couple of times. Yes, the poll was a bit poor; I meant it to be the one or two syllables on the burgh.
As for “berg” - never even occurred to me. I’d never heard anyone say it. One can argue for one or two syllables, but “berg” is definitely wrong and weird. That’s definitely not how the city’s name is pronounced. 
Were you in Balmer Merilin?