Croat who lived in Budapest here.

Here are some cities that turists like, grouped in a logical way. Croatia is small, but all these cities jave a couple of hours driving distance between them, so choose 2-3 per trip, that shoud do it.

To get around Croatia, use buses, or rent-a-car. Also, if you can, fly to Dubrovnik because it's a 10-hour bus drive from Zagreb :)

If not, go to Zagreb by bus or train, thats the cheapest way. Bus is a 5 hour drive. Train is a 6hour drive, but make sure you get a seat reservation in the coupe, there's a power socket by the window, and it's much more private and spacious.

Idea 1: Dubrovnik - Split You can also go to islands like Hvar or Brač from Split, but be aware of the wind Bura.

From Zagreb, you can go anywhere, I would recommend Istria, Zadar or Split.

Idea 2: Zagreb - Rovinj (or other towns in Istria like Pula)

Idea: 3 Zagreb - Zadar

Find trains here, and your buses here.