Hi Jesse,
I want to let you know driving from point A to point B takes a long time in Croatia/Montenegro/Bosnia...and I am a fast driver, very used to narrow/mnt roads.
We spent 3 weeks there last year (going back again in September). For example, a day trip to Mostar: Its doable. but it will take you 3hrs each way with border crossings. We found spending a few days in each location was much more enjoyable.
Since you are planning on driving, you will have to stay outside the city walls with a place that includes parking.
The apartments outside the Ploce gate have the most spectacular views IMO. Most of them are listed on Airbnb. As another poster said: A balcony/terrace is a must. Pay extra if need be!
The downside is there is not much in the way of restaurants there, but you can walk to the old city. Also on that side is a small secluded beach called Sveti Jakov beach that is spectacular. There is a small bar & restaurant on the beach and the prices & food were really good
Apartments outside the Pile gate is really were the city of Dubrovnik resides. We really did not go on that side until it was time to take the ferry (we stayed a few nights on Sipan)
One other suggestion: Stay during the shoulder season. We went in May and the weather was spectacular. Very little crowds.