Where must I go in Croatia?

If you are looking for a great night life i would suggest  island  Pag or more precisely the Zrce Beach .  Or  Korcula for some great architecture to see  and museams. If you are visiting Krk go to Baska - very nice beach.

Dubrovnik is a must. The coastline going north is amazing. Split is worthwhile too. Take a ferry to Vis! I would do Zagreb for a couple days. And if you have time, check out the relatively near Plitvice Lakes National Park. That place is amazing. 

Dubrovnik is an amazing place.  A medieval walled city right on the water.  Split is interesting as well, but if you want to get to the coast, try to make it to Hvar.

we loved Zagreb, and would suggest visiting one of the islands if time allows ( Brac was great)

Umag is not so nice. Better go to Rovinj. Or island Hvar and Brac , you can easily travel by ferry from Split.

I loved all the answers above as well.  But if you can stretch your time a little, I would definitely go to Slovenia and, especially, Lake Bled.  One of the most beautiful places I have been.Lake Bled

And, you can stretch your time a little more, then I would suggest Kotor, Montenegro, and the bay there.