3 week backpacking trip Summer 2011

If you stick with your list of places you want to see for sure that's already about 17 full days in each city. Now add in the day you arrive and the day you depart (both of which are pretty much a wash for any sort of sightseeing), and add in the time lost traveling from city to city, or country to country and you pretty much should not try to attempt any additional countries. If you have some extra time, use it to stay longer in some of the cities you must see, or use it for day trips outside of those major cities so you can see a little bit of the countryside, too.

As far as the order of countries to visit, check flight prices. You may get a better rate for your tickets if you enter through certain cities that you can get a non-stop flight to from Atlanta. And definitely fly open jaw into one city and out of another so you don't waste any time backtracking to your original point of entry.