This rather surprised me. A best-selling novel of 2008, which traces the history of a specific historic artifact, which originated in Barcelona but has been in Bosnia for more than 500 years; it's by far the most owned book set in Bosnia on either LT or GR, and is the most tagged "Bosnia" on LT (and second on GR). I hadn't actually heard of it, which maybe shows the extent to which I took my eye off the Balkan ball after 2007. It is:
People of the Book, by Geraldine Brooks
The second-ranked book, also published in 2008, deals exclusively with the recent war and its impact on Sarajevo. Although it is a novel, it clearly references one particular person; its subject foudn out only after publication that he had become the main character in a best-seller, and was not at all happy about it. The book is:
The Cellist of Sarajevo, by Steven Galloway
In third and fourth place are two books by actual Bosnians. The most tagged "Bosnia" on Goodreads is also third-ranked by ownership there, and fourth-ranked by ownership on LibraryThing. It is the story of a Bosnian town through the centuries, written by Bosnia's only winner of the Nobel Prize for Literature. I actually prefer his book set in Travnik during the Napoleonic wars (which has been translated into English with various titles), but I can accept that his best-known book is:
The Bridge on the Drina / На Дрини ћуприја, by Ivo Andrić
Third-ranked by ownership on LibraryThing, and fourth-ranked by ownership on Goodreads, is a book whose author I actually know personally; we were briefly professional colleagues for a few months in 2002. Inspired by Anne Frank, she kept a diary of her experiences during the outbreak of war in the 1990s; unlike Anne Frank, of course, she lived and is now a film producer in Ireland. Her book is:
Zlata's Diary / Zlatin dnevnik, by Zlata Filipović
Bubbling under: Joe Sacco, Alksandar Hemon, Meša Selimović and the usual suspects.
NB that I didn't find anything much set in Herzegovina. I fear that the best-known book (and that's not saying much) set in the old duchy is a purportedly non-fiction account of engaging with mystical visions. It is:
Medjugorje: The Message, by Wayne Weible
Mostar, alas, doesn't seem to have inspired the same literary frenzy as Sarajevo, though it also had a truly wretched war experience.