I agree with Mathews. There are several interesting things around Zadar, but they’re often more or less accessible by public transport. The city itself offers a striking contrast between the new and the old, with some brutalist architecture right in the old center. Dubrovnik’s (small) walled city center is more cohesive.
At both places, you’ll be offered day trips to spots that aren’t easy to reach by ‘normal’ public transport (Plitvice and Kornati for Zadar, Mostar and Kotor for Dubrovnik). Personally, for a week of sightseeing and exploring the area, I’d pick Split—a bigger city, much better located for visiting the major islands, close to Trogir and Šibenik/Krka, and where you can still do some of the same day trips (Kornati, Mostar… even Plitvice).
As for Plitvice Lakes (and Krka), given how crowded they get, it’s tough to have a nice experience if you arrive midday—which you inevitably will if you’re staying elsewhere and don’t have a way to get there super early or stay until closing. That said, you didn’t mention when you’re traveling; off-season, it’d be less of an issue for that.
