West of Golden Horn

Mosques

• I visited most of the mosques in Istanbul. They all have some special feature like the biggest (Suleyman the Great mosque), the first one (Fatih Mehmet Camii), baroque style (Laleli Camii) etc...

City walls

• From Carye Camii you could follow the city wall by foot till you get to the Golden Horn. You will pass the Konstantin Saray on your left side, the only Byzantine palace left. But all you can see are some walls, nothing special.
• From the Golden Horn, you can take a dolmus to Eyüp, or you could take a boat to Eyüp.

Eyüp and Pierre Loti Café

• Eyüp is off the main tourist track in Istanbul. You were allowed to see the tomb, it's nice to see all the pilgrims visiting the place
• To go to Pierre Loti Café, take a small but steep road on the north side of the mosque. Keep left all the time, turn right at the first house. The walk is 20 to 30 minutes, but is rewarded with a nice view on the Golden Horn.
• From Eyüp you can go back by boat to the center of Istanbul. You could also make a stop at Balat where they have a Bulgarian iron church, nothing special though.

East of Golden Horn

• Definitely recommended is a boattrip on the Bosporus
  
  You can either take a long trip which leaves at the Galatabridge twice a day at 10.35 am and 1.35 pm. The trip takes 6 hours, 2 hours to go, 2 hours stop and 2 hours back. During the stop, you can either walk up to the ruins of the castle, or you can just relax and have a sandwich with fish. The trip costs 3 US$ on weekdays and 6 US$ on weekends.

  If you have less time, you can take a shorter trip from Eminonu to Besiktas. You will have a nice view over the city and the Dolmabahce Palace.

• If you pass the Galata bridge, you can take a small but steep road to the Galata tower. About halfway, turn right down again. After 50 metres you will come to the official red light district of Istanbul. It's a dead end street, the entrance is guarded by 2 policemen. Women and children are not allowed.
• The Galata Tower can be visited. There's a tramway up if you don't like the steep walk up. Entrance fee is 2 US$.