Head up the first set of stairs and smash the door to the right - behind it is a chest containing experience. Eventually, you'll reach the square, where a Cyclops will come to attack. Many citizens of Athens are running around the square, so kill them whenever you're running low on health. After killing the first Cyclops, another will appear and then a third. After killing them all, go through the doorway that has just been opened.
Turn the corner and you'll see a woman down the hall. She'll run away from the sight of Kratos, but continue after her anyway. In the next room, you'll find many different wall panels with artwork of soldiers and other Greek figures. Some of these panels look weaker than others. Smash the ones that look like they're about to crumble for some chests. After finding all of the hidden chests, continue through the building to reach a patio area. Jump to the patio across from yours and watch the cutscene. After the cutscene, chase her up the stairs and she'll fall to her death. Before jumping down after her, head to the left to find a chest on a lower patio. Then jump down and take the key on the corpse.
Go back through the building, this time fighting off all of the monsters in your way. When you reach the patios, this time, instead of jumping across to the other, break through the door in front of the path. This leads you to another room similar to the one with the breakable walls. Fight all of the monsters that spawn and then break the weak walls. After you're done with this, go back to the staircase where you chased the woman off of the patio and jump to the other side of it. Unlock the trap door with the key by pressing , then open it up by tapping . Drop down, take the left path, lift up the gate with , then walk of the stairs to the Rooftops of Athens.