East Coast USA to Slovenia/Croatia

The Star Alliance airlines can get you to/from Ljubljana, Zagreb, and Dubrovnik with one connection each way. Try a search through Lufthansa. I don't see any connections from Montenegro (using www.skyscanner.com) and any way, if you have a rental car, you'll probably want to both pick up and drop off in Croatia, to save money. If you want to use the same car in Slovenia, too, then that might mean flying to Zagreb first. Otherwise, Ljubljana-Zagreb is a direct, 2-hour train ride.

Some routes with 2 or more connections may be cheaper on other airlines, but beware of unprotected "self connections" between airlines that don't cooperate with each other.

There is an AA flight to Venice with a plane change in Philadelphia.
Otherwise check out https://matrix.itasoftware.com/

I always start with a Kayak search. Zagreb is usually going to be your best bet, and if you can't fly open-jaw, it is well situated for a somewhat circular route. (Into Zagreb and out of Dubrovnik would be ideal, unless you can get a Ljubljana deal.)
Train is extremely limited in Croatia, buses and ferries are the way to go UNLESS you are going way off the beaten path or exploring inland Istria.
Have you consulted a guide book yet? What has stood out? What are your interests?
Late May/early June is a wonderful time to visit. Sea may be a little chilly, so I would put any place you wish to swim on the later end.

Frankfurt is well connected to all of these cities. Look for a flight through there. Easy.

Thank you. How would you suggest getting from Frankfurt to Slovenia?

Diane, I believe David was suggesting choosing a route that goes through Frankfurt. Have you plugged your desired flights into a search engine yet? It is best to deal with specifics and not hypotheticals--I like Kayak but there are several to choose from, then I purchase directly from the airlines. Lufthansa is a good option, as 1 suggested--only one place change to get to Zagreb and Dubrovnik! And if not Ljubljana, it is a short train ride to Zagreb from there.

I think David means that you should be able to find flights from Charlotte to Ljubljana, Zagreb, etc., with a connection in Frankfurt.

I see a non-stop from CLT to Frankfurt.

Be extremely cautious about trying to save money by piecing together an itinerary booked on separate tickets. That puts all the risk of a missed flight on you. It is much safer to book Charlotte to wherever, with a connection in Frankfurt (or Munich, Amsterdam, etc.), rather than two separate flights CLT-Frankfurt and Frankfurt-wherever.

It's worth looking at departures from Atlanta or Raleigh-Durham to see whether they would save you substantial money.

Edited to add: I see that there's a non-stop from Dubrovnik to Philadelphia.

If you can fly into Venice, there are numerous good connections to Ljubljana these days: GoOpti, FlixBus, and even a train through Trieste now. These options did not exist the first time I had to get from Venice to Ljubljana years ago.

Otherwise, Zagreb as mentioned above works too, though the last two times it has been Venice for me to get to Ljubljana.

That Dubrovnik to Philly AA flight is also new - starting next year. I may use that option if I go back, because PHL usually works for me as a good connecting airport.

There is an Adria flight between Dubrovnik and Ljubljana now as well, if that helps you at all.

I am making the trip mid June from Philadelphia to Venice direct flight American Airlines, staying in Venice 2 nights then I got a direct flight from Venice to Split for a whopping $52 usd.