Athens to Dubronik

Best would be to fly, though you may not find many budget options. Transport between those two cities continues to improve, but given that you are going between an EU and Non-EU countries, that both are competing tourist destinations, and historical political issues have meant limited border traffic, it is still difficult. Political issues in Albania (improving though) and a lack of international rail make a land crossing difficult, but not impossible. Buses are an option, a rental car likely not. For bus info, do some searching on Lonely Planets Thorntree Forum and search this forum, there have been a couple of postings. There is no direct ferry, it is possible to take a ferry to Italy (Bari) and then to Dubrovnik, though you are looking at two nights of travel minimum. Air is the other option. There are direct flights, or at least going through Zagreb, but not on budget airlines or Aegean. Croatia Air is the most likely option. You could do the same option though as a ferry, take a flight to Italy and connect to a flight to Dubrovnik. You could look into Vueling as well as Aegean. You can also play around on Whichbudget.com, that would give you airlines that fly to those destinations.

If you have a couple of days to spare for this trip, you can make an adventure of it. You can find relatively cheap airfare from Athens to Tirana, Albania. You can find buses from Budva, Montenegro to Dubrovnik. So the missing piece is the how to get from Tirana to Budva. This would be a good question on the Thorn Tree forum. We made this trip in the opposite direction (Dubrovnik>Athens) a few years ago. We bused to Budva and found a tour company offering a day trip to Tirana. So we signed up, had a nice tour of Albania on our way to Tirana, and just got off the bus in Tirana (skipped the return to Budva). It took about 3 days: most of a day for the bus to Budva; most of a day for the bus to Tirana; and then part of the next day for the short flight to Athens.

Thanks Paul, Matthew, and Charlene! It's interesting that there are still pockets of difficult-to-navigate through areas in Europe, but then I remember when I started traveling through Europe, you wouldn't have dreamed of going to Bulgaria, Poland, or anywhere else east of WEST Germany! I like the ferry to Italy then ferry to Dubronik idea - I should have mentioned that I asked this question on behalf of my 20 year old daughter! Thanks again - I appreciate your input!
Dianne