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There are a number of interesting sites within Baku's walled fortress, the Old City (a UNESCO World Heritage site), which can all be seen on foot in one day:
The Palace of the Shirvan Shahs. 10AM-5PM daily. The medieval palace of the Shirvan Shahs is the highlight of the Old City and a must see for any tourist in Baku. 2 AZN. Maiden's Tower (Giz Qalasi). 10AM–7PM daily. This mysterious and eccentric tower was built somewhere between the 7th and 12th centuries and may have served as a fire beacon, defensive fortification, astronomical observatory, or Zoroastrian temple. .5 AZN. Outside the city, on the Absheron Peninsula, there are several interesting sites that are easy to reach via taxi or public transportation. Moreover, the scenery along your route is itself a fascinatingly ugly sight to be seen, a desert wasteland with white salt flats and natural oil pools seeping up to the surface. Atashgah Fire Temple. You can take the Baku Electric train from the Baku train station to Suraxani station for 10 qapik. Simply walk through the station to the outdoor platforms where a schedule is posted. You can also take Marshrutka 213 from Qara Qarayev metro station or Marshrutka number 84 from Azizbeyov metro station. You can pay on board or buy a ticket from a kiosk on the platform. From Suraxani station walk about 100 meters and 'you can arrive at the temple Admission is as follows: children's 0.20 AZN, student's 0.40 AZN, adult's 2 AZN. If you want to take pictures it costs 2 AZN in addition to admission. Yanar Dagh. Yanar Dagh is a mountain that has been continuously on fire for one thousand years. The natural gas vents ensure that hot flames roar out of the sides of this hill even when it rains. There is a small cafe next to the natural wonder that serves tea and snacks. It is best to take a cab as Yanar Dagh is remote and difficult to find. As of Mar 08 the small cafe was just a shell of a building and no longer there.