Qobustan is best known for its rock petroglyphs and mud volcanoes. In 2007, UNESCO included the 'Gobustan Rock Art Cultural Landscape' in the World Heritage list.
Take the number 20 or 288 bus from the old town to dvadsat bus stop (bus number 20 terminates there). Then take the 195 bound for Alat and get off in the town of Qobustan. The museum is a 2-3km walk in the opposite direction of the sea towards the hill with many rocks on. Alternatively, many taxi drivers will be willing to take you there, be sure to haggle for your fare though. The Roman graffiti is on a rock in the middle of a road that branches off from the road at the base of the hill with the museum on it. The area around the museum is good for hiking, there are many dormant or extinct mud volcanoes that have been heavily eroded, making for spectacular scenery. The fare for the museum is 3 manat, plus 6 manat for an english speaking guide.