The two airports worth considering
Zagreb is the usual choice: about 165 kilometres and 2 hours 45 minutes of driving, with the most flights from Germany, Austria and Switzerland. Zadar is a little closer at around 150 kilometres and 2 hours 20 minutes, and usually cheaper if you are flying low-cost.
Both are across the border, in Croatia. That is not a problem — it is simply something to declare before booking, so the paperwork for a vehicle crossing a border is ready in advance.

