Edinburgh is the capital of Scotland and one of the most wrongly pronounced names of places. This mistaken pronunciation isn't only heard in American English, but is also heard around British English as well.
While you may hear different variants of the pronunciation around Scotland, this is due to the different kinds of Scottish accent that exist.
The standard phonetic pronunciation of Edinburgh is ed-in-bruh or ed-in-buh-ruh, as both are considered correct. This can be confusing for speakers in the US who may liken how to pronounce edinburgh to how you would say Pittsburgh.
Variations that are absolutely considered wrong by native speakers in Scotland include Edin-burg and Edin-buh-row.