Montenegro, lucky you. I love it so much I have returned a number of times ... the last was in July.
Okay, public transportation is minimal and not very convenient for tourism, so i recommend a guide with a car (maybe a van for you), good news, the costs in Montenegro are significantly less than Western Europe. At the end I will post an email address for an amazing young lady. Recommended her to another couple about a month ago and they came back raving about her. At the very least you can use her for planning services.
The Kotor Bay area is pretty amazing and there are a number of worthwhile stops. Kotor it's self I think is worth skipping if you have seen Dubrovnik because it is just a smaller version of Dubrovnik; although a lot less Disney Like than Dubrovnik. Otherwise ... go. And if the tour boats are in, there is a way to avoid the mess. Stay in Perast just down the coast and visit Kotor in the late afternoon or early morning before the boats unload. I actually enjoy Perast more than Kotor.
Then yes, Budva for the beaches and the old town, then Stari Bar for the old abandoned city and the wonderful little road lined with shops and pomegranate vendors. Past the "oldest" tree in Europe and down to Ulcinj. The old town on the hill in Ulcinj is really amazing.
Its August and warm as he!! so head inland to the high country. See the monastery at Ostrog and the hotel restaurant below it a few miles with the terrace that looks hundreds and hundreds of feet down into an amazing valley. Great lunch stop.
Further up to the Tara River Canyon, the deepest in Europe. Ride the zip lines shop the souvenirs in the huts along the rim. Brave? Go rafting.
And I haven't even touched the National Parks with spectacular views, mountain lakes, and the prosciutto houses along the way or the mountain roads that will blow your mind.
With 15 days you may want to start in Sarajevo; and experience not to be forgotten, then to Mostar and then on in to Montenegro. The borders are currently (and have been all year) easy to cross. Did I mention the small olive processing houses and the wineries? And add a few days and there are twice weekly flights from Podgorica to Budapest for about $50.
Anyway, you want to contact Dijana at firstname.lastname@example.org. Full tour, transfer assistance or just planning and booking; worth the conversation.