BEWARE Any bus or tram with a sign or indication that it heads for or calls at Topkapı will NOT take you anywhere near Topkapı Palace. Rather, it is going to a neighborhood named after the city gate near which it’s situated “cannon gate”, which may be worth a trip to take a look at the impressive city walls. Topkapı neighborhood is located in the extreme western part of the old city, near the city walls, while Topkapı Palace is located in the extreme eastern part, which means the distance between each other is at least 7-8km. ‘Topkapı’ alone almost always refer to the neighborhood, not the palace. Taking a bus heading for Topkapı to go to the palace is a common mistake made by travellers. For the palace, the stop/station you should look for is 'Sultanahmet'.
On foot
Most of the sights in the old city are close enough to be negotiated on foot, as they are located in or around Sultanahmet Square. For many others, just follow the tram line. However, between Eminönü/Sirkeci and Sultanahmet, it is faster to to take the shortcut through Ankara Caddesi Street and stray away from the tramline as the tramline follows an arch through that part of the city.
The sidewalk along Hüdavendigar Caddesi between Sirkeci, Gülhane, and Sultanahmet Square is not very wide and trams pass along fairly close to the sidewalk, so watch your steps especially when you hear tram's horn.