What is the recommended route, particular sites to see, and a good place to spend the night on a two day drive from Granada to Barcelona in early July?
The natural place to stop is Valencia (500km from Granada / 350km to Barcelona).
I would recommend perhaps a longer route on Day 1, via the delightful Renaissance towns of Baeza and Ubeda
Buy some pottery of Paco Tito. http://ubedaybaezaturismo.com/en/place/pottery-museum-paco-tito/
Peniscola and Tarragona would be worthwhile stops on Day 2.
Honestly, I would leave the car in Granada and fly. Vuehling Airlines has very reasonable flights that take 1.25 hours. My husband and I just did this a few weeks ago.