What a lovely gesture! I hope it all pans out.
I have been to both Dubrovnik and Cavtat. I would recommend Dubrovnik because it has far more 'going on' and good transport links between hotels and the city. Cavtat is close to the airport and is basically a small town/resort.
Whilst they might consider car hire a good way to visit, I would recommend the day tours offered by local tour operators - I took tours to Montenegro and Mostar with Atlas, and found I had plenty of time to explore without hassles of needing to find a car park and, more importantly, insurance issues for crossing the border ... I recently returned from Split where I hired a car and would have had to pay a substantial insurance and hire supplement to cross over into Bosnia had I wished to revisit Mostar or any other towns. within driving range. They could also visit Medjugorje which is a Marian shrine. And they could also visit the islands ... I recommend Lokrum which is a nature reserve with easy paths.
Unless you have big bucks with which to treat them, I think you will find it more affordable to find accommodation outside the city walls/old town of Dubrovnik. There is a good choice of hotels with different star ratings on the nearby Lapad peninsular and a regular and cheap bus service which will get them into central Dubrovnik.
Hope this helps ... and do let us know how you get on.
