The Eyüp Sultan Mosque is situated in the district of Eyüp near the Golden Horn. Mosque and Tomb of Eyüp Sultan are considered as the holiest place in İstanbul. Eyüp Ensari was a companion of the Prophet Muhammed, died during siege of İstanbul by Arabs in 674-678 and was burried here. Fatih Sultan Mehmet the conqueror found the grave of Eyüp Ensari and built a tomb over it, then a mosque and religous complex nearby.
Google Maps - Eyüp Sultan Mosque

After conquest of İstanbul, Fatih Sultan Mehmet's own mentor saw the site of Ensari grave in his dream. Then the first mosque is built. The orginal mosque, dating from 1458, was enlarged by Murat III in 1591. Ahmet III (1703-1730) replaced two of its minarets.

You can use Metrobus : Take off Ayvansaray station then you can walk for 15 minute to go or use taksi after metrobüs.
You can use Public Bus
İETT Şehir otobüsleri - Eyüp

There are notable for the vast numbers of cemetries, tombs of the ottomans, for its founains, baths, mosques and minarets.Outside of Eyüp Sultan Mosque you can see lots of piqeons.You can do shopping Eyüp Sultan square and buy traditional gifts.Dont forget camera, lots of view to take photos.