What are the driving route from Zagreb to Sarajevo look like? Are there any must see locations on the driving route from Zagreb to Sarajevo? Whats a good timeframe to travel across the border to avoid a long border crossing queue? Also, Is there a fairly straight driving route from Sarajevo to Montenegro coast?
I can't vouch for a lot here, but you should see Split and Mostar, which are...sort of out of your way..southwest from Sarajevo, basically. Lots of history and beauty - or at least before. I was very little, but I still have a few images in my head..I don't know how they are now. Look them up!
Use yahoo map to find the route....
Just want to add a few remarks to Latarina's suggestions.
You can skip Split, it's 'just a large town', nothing special really. Better add Zadar and Dubrovnik to your itinerary in Croatia. Mostar in Bosnia is worthwhile, just like Medjugorje (north of Mostar) in BiH.
Heading SE from Dubrovnik, there's a small border crossing to Montenegro. You will pass a nice campsite at Molunat village, a good place to spend a few nights.
Once you are in Montenegro (in local language: Crna Gora), do visit Kotor (and the lovely bay around it) and Budva. Both are very nice historical towns, but quite touristic. If you're fed up with that, head for the inner country of CG and go to Zabljak. There you will find the Durmitor national park, miraculous natural beauty. To cool down from the heat there during the day (nights are cold there, though) have a swim in the Biogradsko lake, situated SE of Pljevlja.
Happy touring around the western Balkans!