Our cruise arrives at 11am and departs at 10 pm in Dubrovnik and I really want to take a tour to Mostar but don't want to pay the ships price for the excursion. Viator offered day trips there, but they left at 8am. Any suggestions?
If your cruise offers an excursion, that's probably the only safe way to do it, because the border crossings can be really unpredictable - I've done 4 border crossings in that area and it's taken anywhere from 5 minutes to 3.5 hours.
It's a 2.5 hour drive, so that's 5 of your 11 hours right there (with no traffic problems).
You might be able to do it with a private car hire (they usually know the quickest/least busy crossing), but I can't imagine that will be cheaper - plus if you are on a tour from the cruise, if you are delayed you'll be sure not to miss your departure.
I would spend the day in Dubrovnik. If you don't want to do any of the many historical tours/check out the old town, I would recommend having a day at the beach (there are showers/lockers/changing rooms) and then spend the money you saved on dinner at Nautika. Be sure to make a reservation (ask for an outside table across from the fortress) and order the truffled pasta :-)
We stayed in Dubrovnik last year and took a day trip to Mostar. We used a private tour, and even staying in Dubrovnik it was a really, really long hot day. On the way there, you have to pass through border crossings and it just depends, it can take hours. Mostar was interesting, but not worth the trip in my opinion and also my kids ages 24 and 25 felt the same. Dubrovnik is absolutely beautiful. There are loads of cute restaurants and we took a boat trip to other islands that was the highlight of our trip. I really would not recommend trying to get to Mostar.
You can get to Kotor (Montenegro) by public bus from Dubrovnik. Googling will probably turn up the schedule, but be conservative in your plans for the return. Also, verify that you're looking at the schedule for the right day; Saturdays, Sundays and holidays are different.
Kotor has been called a "mini-Dubrovnik" on this board, which is probably accurate, but the road skirts the magnificent Bay of Kotor.