Itinerary Question

If you are going to Croatia and into nature, do not miss Plitvice National Park. In Slovenia there is Lake Bled which is an excellent place to visit and there are the Julian Alps in Slovenia.

Are you planning on renting a car or using public transport?
The answer really depends on the places you choose and your mode of transport, but in general, yes you can choose four bases, such as Zagreb-Plitvice-Split-Dubrovnik for example, which is rally easy by public transport.
Since you are a nature lover, you should look into the many national parks in Croatia, as there are many options. We visited four times without a car, and did a fair bit of hiking, but next time we hope to drive.

Thank you for your quick responses. We really don’t want to drive while we are there. We would like to take public transportation or hire a tour guide for the day.

Okay that is helpful to know. Some of the parks are easily reached using public transport, some are not. You may also want to visit islands in June, which are well linked by ferry and catamaran and offer plenty of nature time (we often just set out on walks along the seaside). So I would first work out how much time you want on mainland vs islands. And of course the Croatia-Slovenia split as well, as you could spend two weeks in either country and see only a fraction.

You can, and it’d be more like three: Dubrovnik, Split and Ljubljana. This would include more organized tours (private or small group) than DIY. Transportation is the major hurdle in this region. Distances between sights are usually significant, and it’s lacking the kind of robust public transport system you’d might see in more Western European countries. Effectively, you’re relying on these organized tours to fill that gap.

In June, tourist season is getting to full speed and each of those cities will have a constellation of options. Dubrovnik boasts a lot, including trips into Montenegro, Bosnia-Herzegovina and plenty of excursions to nearby islands. Split is a launch point for nearby islands, and the closest major city to Plitvice. Unfortunately, seeing Plitvice as a day trip in June is about the worst time you could get, with peak crowds in midday. Ljubljiana is basically smack in the middle of Slovenia. You can get anywhere within a couple hours, making tours of the Alps and elsewhere very realistic options.

It must be noted too, the major islands of Korcula and Hvar lie between Dubrovnik and Split. These are great destinations in their own right and deserve a couple nights. They’re also well connected by fast and comfortable ferries. They also serve as launching points for various small excursions.

If you want to see Plitvice National Park, you really need to spend a night at the park. Otherwise, as already suggested, you'll have a dreadful daytrip experience, because the park gets absolutely slammed during daytripping hours. I'd skip the park if not willing to devote a night to it.