First on the list Gazi Husref Bey’s complex, and his list of endowments.
Along in this complex you should NOT miss:

Gazi Husrev beys Mosque, fountain
Some 100 meters away from Gazi Husref bey’s complex, down the Ferhadija street, you will find the Ferhadija Mosque. Mosque with, most probably, most valuable interior decorations of all mosques in Sarajevo.

Ferhadija Mosque
Emperor's Mosque, built by the founder of Sarajevo, Isa Bey Ishaković. Named in 1462 in honor of emperor of Ottoman empire, Mehmed II Fatih.
One of the oldest mosques, if not the oldest one in Sarajevo, Magribija Mosque, built by Šejh Magribija.
Just one block away from the Magribija Mosque, another one, younger indeed, but maybe the best proportional one in Sarajevo, Ali Pasha Mosque.

Ali-pasha Mosque, interior
Just outside the old part of the Sarajevo, on the small hill you shall find the most interesting cemetery, the oldest Muslim cemetery in Sarajevo, Alifakovac Cemetery.
Keep in mind that in our Religious Sarajevo section you can find many many other attractive point in ranging four world religions.