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There is a free bus from the city centre to the border!! Theses buses belong to the casinos you can find at the border just before Gevgelija. You can find theses buses on Tsimiski street. They are easy to recognize (the name of the casino is printed on the bus, and it is written "free shuttle"). I didn't take it but I was picked up by a guy working at a casino who gave me the information. Another nice information: you can eat and drink for free at the casino!! Apparently you can just show up at the reception, they will give you a card and you can enjoy food and drinks for free!! I did! Anne-laure, may 2013"
Take a bus #8 (or #31?) from Egnatias street in the centre to KTEL (last stop). You can also take bus #45 which goes between KTEL Makedonia and KTEL Halkidiki (you want to go to ''Makedonia''). Then switch to bus #81 which you can find on the upper platform. Afterwards, you can do different things. You can get off at a first bus stop after you drive over the highway Athens-Skopje - [http://g.co/maps/3qj6m here]. Be careful, the first big crossing you going to come to is the crossing with the ring road (you are going to driver underneath it) while only the next on is the one you need (you are going to drive above it). Then you have to walk almost 2km backwards (if you walk fast it takes 20 minutes) and you can hitch on the junction to the highway to Skopje. However, if the bus goes into Agios Athanasios you can better get off and find your way from there (it seems that this bus goes differently depending whether it is #81 or #81A and depending on some external stuff; you can talk to the driver to make sure).