You can start by exploring transportation links on Rome2Rio. (Do not, however, trust its time or fare estimates.) Greece to Montenegro to Croatia will mean buses if you do not fly, and flying is almost certainly going to introduce you to airports not on this trip's wish list (hello, Vienna? Budapest? Munich?). Check skyscanner for flights, being aware that flights may be day-specific.
When Rome2Rio suggests a bus option, keep drilling down till you reach the name of the bus company. Usually there will be a link. If you dont' find one, try Googling "bus Kotor to Dubrovnik), etc. For buses to, from or within Croatia, the BusCroatia website seems helpful. I haven't been to Greece recently, but the buses in Montenegro, Croatia and Spain were quite comfortable.
Border-crossing buses are infrequent, so pay particular attention to their schedules, and double-check those schedules as soon as you get to the departure city. Do not wait until departure time to buy a ticket on an international bus.
Suggested destinations in Montenegro: Cetinje, Ulcinj, Budva (similar to Kotor, though, so not mandatory), Kotor, Herceg-Novi, quick stop in Perast, Lovcen National Park (transport permitting) and possibly Lake Skadar. I found the capital, Podgorica, distinctly underwhelming, but it was a convenient base for side-trips to some of the above destinations. It may well be an unavoidable stop for reasons transportation.
Suggested mainland destinations in Croatia: Dubrovnik, Split, Zadar (somewhat reminiscent of Dubrovnik, so skippable), Istrian Peninsula, Plitvice Lakes National Park (top recommendation; stay near park the night before visit to beat the hordes of day-trippers onto the walkways), Zagreb.
Spain: I highly recommend Cuenca, which is an affordable and quick train trip from Valencia if you buy the AVE ticket early; otherwise, it will be painfully expensive. If you have access to a car through your friend, I also recommend the charming and unvisited-by-Americans Teruel. There's also bus service that seems to take less than 2 hours. An overnight in Teruel would be pleasant. Well, except for the heat; brace yourself for that. There's fast train service to both Barcelona and Madrid from Valencia. Which direction you go depends on your personal interests.