I like the islands and the coast a lot, although my family is not from there. My favourite islands that I went to were Rab, Pag, and Krk.
Split and Zadar were both quite pretty when I went there.
Zagreb seemed nice, although I've never spent more than a few hours there.

It's been a long time since I've been back, so I'm probably forgetting other places I thought were beautiful, but I don't remember. The national parks are worth checking out if you have the chance.

Where is your family from? I see you live in Canada. :)