Ten days just isn't enough to include Mostar and Kotor, especially if you're prioritizing beach time on Hvar, Brac, Vis, or Korcula. Your proposed day trip, in June, going to either will take about 3 hours each way, especially if the borders have lines. Don't underestimate Kotor and Mostar, though. Mostar is culturally and religiously distinct for the region. If you want to see just the Stari Most and Coppersmith Street, a one day bus trip would be enough, but an overnight stay gives you a chance to enjoy the town more, especially with a guide. The mosque, museum of Herzegovina and new Muslim cemetery were all worth the time. The mosque was not out of the ordinary, but the Imam spent more than an hour with us answering questions about the religion and Islamic culture, as well as about the mosque and school attached to it. We were the only visitors at the Museum that day, and the director gave us a personal tour. It was such a wonderful way to learn not only about the history and development of the region, but also the war years. We found both the Imam and museum director to be very happy to share their knowledge and experiences, and definitely got the impression that most people don't ask.
We also liked Montenegro very much, although we were only there for a few days. We spent a full day just in Kotor wandering around the town, visiting the Cathedral and reliquary and an orthodox church among other stops. For our second day, we hired a guide and driver we felt and it was a good buy, although it did cost a couple hundred Euros. The Boka Bay drive is scenic and the advantage with a driver is that you can stop anytime you want for photos. Our day also included Njegusi and Perast. It was a long day, 0900 - 1800, but really interesting, especially with the our guides (the driver was actually a guide in training, so he was also full of information). Unfortunately, in Perast, we had time only to see Our Lady of the Rocks, but we like to take things a bit more slowly and soak it all in. We didn't have as much time as we wanted to walk around. If you decide to go to Kotor, check the cruise ship schedules -- it's an increasingly popular stop for several lines. The town is very tiny and compact. Adding 3000 cruisers would definitely be unpleasant.
Personally, I'd choose Split over Dubrovnik. Dubrovnik is pleasant enough, but overrun with tourists and cruise ship passengers. I was there about 10 years ago, and I think it's become an overrated circus. The wall is fun, and the Stradun is just OK. Taking the cable car up to the overlook is nice and the museum about the war is well-done. There's also a cultural museum that I enjoyed. An ambitious vacationer could do it in a day or at a max, two. In Split, I found Diocletian's Place interesting, but enjoyed the archeological and cultural museums more. While you can't enter early in the morning, I went to the area shortly before dawn for some wonderful photos and peace and quiet. Like everything else when traveling, what's "best" just depends on your interests.