Flight destination city

Out of these three cities Prague is probably most of the time the cheapest to fly from the US. Otherwise is usually London. Point to point would be probably cheaper than rail pass. Car rental is expensive in Europe as is gas but it may be cheaper than train for 5 people especially if you return the car at the same place where you rented it.

Check out Amsterdam for your arrival. Do you realize the distances and time involved? Ambitious. Check Ryanair and Wizzair.

Car vs rail pass. A car would give you more freedom, but you will need a car big enough to seat 5 people comfortably for long distances AND store all their luggage. Google maps shows 1300 kms (that's 800 miles, and I'm guessing it isn't all flat, straight highway) from Dubrovnik to Prague. Michelin maps shows two routes (via Zagreb or via Budapest) with a NET driving time of 13.5 or 15 hours. There may be a huge -off fee for returning the car in another country - IF you can even do it. Look at the websites for 3-4 main car rental agencies, that will give you an idea. Michelin maps also gives you estimates of gas costs and tollroad fees. Then price the rail pass for the length of time you expect to be traveling. Flying open-jaw is usually the best option, so I would start by looking for airlines that fly to Prague, Dubrovnik and the U.S. But Dubrovnik isn't that easy, so you may find it better to fly round-trip to Prague and then a cheap flight to Dubrovnik. See this topic http://www.ricksteves.com/graffiti/helpline/index.cfm?topic=25948

Thanks for the helpful advice!

If its just the coast you are after you might look at Varna instead of Dubrovnik. You can fly direct from Budapest.

Cars across borders are expensive. There is no train to and from Dubrovnik. That is accessed by bus, car or boat. Dubrovnik is really quite a stretch from the other two unless you are willing to either drive or make several connections and stops. Consider Budapest, a phenomenal city.