Croatia Itinerary

Maybe check first where it makes the most sense for you to fly to, then we can suggest things en route. Split is the obvious one to check. Have you determined how many days you wish to stay on Vis? I would recommend at least three nights, but you mgiht want more for your family reasons.
You could fly into Split, visit there, Vis, and fly out Dubrovnik--possibly visit one other island if you like to move fast. Or, tack on the Montenegro visit if you get your island fill with Vis.
See the catamaran routes on the Krilo and Jadrolinija websites.
If you fly in or out of Zagreb, you could visit there and Plitvice.
There are not a lot of cities in Croatia--mostly very small towns.

Some observations from a couple of trips since COVID.

Zagreb: nice town for arrivals, pleasant for a night or two, but a bit far from Vis and Split.

Plitvice Lakes: for my enjoyment relative to the rest of the trip .... arrive as early as you can, do 3 hours, move on. Although others spend 2 days, it wasn't so moving for me that I would do that.
Vis, no help, never been. Looks like a nice escape from Croatian over tourism.
Split: my visit 10 yeas ago was very enjoyable. My two summer visits since COVID I didn't enjoy the drunk European trust fund brats on holiday. I was happy to leave after 2 nights. I have stopped in Omis and Baška Voda and if i were to return to the area i would do a day tour of Split as there is a lot interesting. But sleep in Baška Voda or Omis, or someplace similar.

Dubrovnik: Despite being so incrediably touristy for some reason I enjoy the heck out of it; and its beautiful. But 3 nights is enough.
Cavtat: a splendid alternative to too much time in Dubrovnik and in the right direction.

My preference is Montenegro. So, continuing down the coast
Herceg Novi: great old town for a lunch break and a tour.
Perast: easily one of the sweetest settings and enjoyable overnights in the Balkans.
Kotor: a facinating old town, but after Dubrovnik maybe a day tour before you drive over the mountains to Budva.
Budva old town is a pretty relaxed and enjoyable stay.
Stari Bar: a 500 year old abandoned city Facinating place and a good place for a traditional night stay.
Ulcinj and Shkodra Lake amazing, simply amazing, and not far from the Podgorica airport for your trip home.

Research each and see what lights your fire then post that and you will get more detailed assistance. Otherwise its going to be generic help and we can do better than that.

There are a lot of video links here
https://community.ricksteves.com/travel-forum/montenegro/a-week-trup-report

I would work backwards

You will be going to Vis for a certain number of days.

You get to Vis via Split, which is very worthwhile place for a couple days.

You also want to go to Montenegro, which you can do via Dubrovnik, which is also worthwhile.

Between Vis, Split, Dubrovnik, Montenegro, that could easily be 10 days. But to pad things out, I would focus on places near Split or between Split and Dubrovnik.

Near Split there is Trogir, Primošten, Šibenik, and NP Krka. You could do Plitvice from Split but it would be a long and complete day. If you spend a night in Split area on the way back and fly from Split, Trogir would be a good place to stay.

Between Split and Dubrovnik there is Brač, Hvar, Korčula, all easy enough to do via ferry. Makarska, Omiš may be worth a look on the mainland but I'm not sure they fit your criteria, you might enjoy Mostar more in Bosnia if you rent a car from Split.

From there you would fly in and out of Split and/or Dubrovnik and things should fall into place once you make the booking: Vis from Split, Montenegro from Dubrovnik, other places in between.

Ivan, so glad you are in thr club. If the OP were to want some sort of beach resort within about an hour of the Zadar Airport, would you hsve any suggestions? Okay, I confess, sorry trishazuanich, I just got news that I have to entertain someone in 2 weeks. But maybe what I find you might be interested in.

My husband and I traveled to Croatia in late May of 2017, so it's been a few years, but the trip was terrific. We stayed in 4 places, 3 nights each. We flew into Dubrovnik, stayed in a B&B inside the old town but skeddadled out to avoid the cruise ship crowds in the daytime. Took the water taxi to Lokrum one day and took a wine-tasting tour on the Pelejsac peninsula the second day. We still had plenty of time to wander around the old town in the evenings and early mornings. After the 3rd night checked out of Dubrovnik BnB and picked up a rental car which we drove up the coast to Zadar. Stayed in old town Zadar, walked to the sea organ and solar installation for sunset. First full day we drove to Plitvice, had a wonderful time even with lots of people. Second day we explored old-town Zadar, the ruins, sculptures, marinas, and the glass museum. Third day we drove back down the coast to Split where we turned the car in and caught the ferry to Vis. Took a terrific boat tour on the first day that took us to various caves, grottoes, beaches and even an old communist-era submarine tunnel. Second day we walked and hung out at the beach. Caught the ferry back to Split and taxied to Trogir for our last 3-night stay. Day one caught the ferry from Trogir to Split and explored the ruins there. Day 2 we wandered around Trogir. Taxied from our Trogir hotel to Split airport on our last day. Our itinerary was dictated by needing to fly into Dubrovnik and out of Split, so we didn't have time to get up to Zagreb as we would have liked, but the itinerary turned out to be a great success and I would happily do it all over again. One note: when we visited Zadar, cruise ships had not yet descended upon it. I wouldn't stay there on days when a ship is in port.

Thank you all for your reply, and happy to hear someone commented about Vis! Honestly I have no idea how many days to spend there but it sounds like the best plan is to fly into Split/Dubrovnik then out of the other. Nice to hear that it most likely won’t be too much for 10-12 days, and maybe tacking on some time in Montenegro. A couple questions, how much time would one want to spend in Montenegro? Also, is renting a car better or train, or a mix of both to get around?

You could do Montenegro in a day trip or spend a couple of days there.

With a couple exceptions which doesn't matter you are going nowhere near any trains. Either rent a car or take bus or ferry.

A couple questions, how much time would one want to spend in Montenegro? Also, is renting a car better or train, or a mix of both to get around?

Up above I put a link to some videos of places in Montenegro, I suggest you find similar on the places you are interested in, in Croatia. For example, here is Vis and its stunning: https://youtu.be/-k5OIMR0RBI?si=W7R0Jfln_pxTaFX4 I would want no less than 3 nights. Thats arrival day and two full days before you leave on the fourth day. You have time so look at videos and see if something lights your fire and then plan around that. It's not about Croatia or Montenegro, forget the borders and choose what interests you.

For getting around as Ivan pointed out, there are no trains where you are going. You could rent a car, but then it gets real expensive unless you do a round trip and return the car where you got it. Round trips are often a waste of time, repeating the same route twice. You could ride the bus. Nothing wrong with that. They might be a little more basic than the rest of Europe and you are saddled to their schedule and their stops. Best, if you can afford it, will be private drivers. Its what I did on my last trip to Croatia a few years ago. I just got back from 7 days Bosnia a few days ago and the cost of the drivers didnt break the bank. Paid off too when I pointed out the window and said, look at that ancient village!!!! Three minutes later I was walking the streets of the village on an unplanned stop. If you need help with drivers or any of the planning, I have a good source.

Come back with the places that interest you and let see if they can be strung together in the time that you have. But make it 16 days as thats Saturday through Sunday over two weeks.

Vis is very small of course so it really just depends on your interests. I would want no fewer than two full days (three nights). The beaches are amazing, and riding a scooter around is great fun (or you can rent a bike, which I would do now that we have e-bikes). Otherwise, we did a little hiking--up to "Tito's cave" and scrambling down to beaches.
Montenegro is going to depend on how much time you have left. A few days would give you time to see the closer parts like the bay of Kotor, and that is easy by bus. Rent a car if you want to go to the mountains. First decide how much time you would like to spend in Croatia--if you include Split and Dubrovnik that eats a few more days depending on how fast you like to move. You also have the mainland in between and all the other islands to tempt you.