Gjirokaster is a city in Albania. City located in the mountains in southern Albania. The famous dictator Enver Hoxha was born and spend his child hood here. The view for the Mountains and castle is beautiful and the old city which is located uphill has very picturesque white wall houses.
It is very easy. Go down to SH4 and go Northbound. You need to go around 500m away from the bus station which is next to the crossing of SH4 and Bulevardi 18 Shtatori street. This is to avoid stopping taxis which you do not want.
It is not the easiest way. You can easily hitchhike to Tepelenë on SH4, however, the problem starts afterwards. You should ask to drop you before Tepelene, on the SH75 crossing (you can recognise it easily as there is a bridge). Usually not many cars go there, if so, they usually head to Përmet. In Përmet, everyone usually heads to some villages nearby or the Greek border near Çersovë. It is recommended to hitchhike without a board to catch short distance lifts. Few cars head to Leskovik and it is a mountain way. It is also possible that you will have to walk. If you were lucky to get to Leskovik, the rest of the way up north may be easier. Head north to Ersekë, and finally to Korça. It is a longer way than it seems to be as it goes via mountains. This makes it be, however, definitely one of the most beautiful in Albania. It is still worth trying, but get prepared. Start very early. Make sure you have enough food and water (useful if you get stuck in the middle of the way nearby Greek border or somewhere in the mountains) and it is better to have a tent in case you don't make it.