Galata Tower
It was built by the Genoese on the city walls of Galata, then a western Genoese/Venetian stronghold beside eastern Byzantine/Ottoman Constantinople. Ride an elevator to the top 20 TL, then walk the parapet for a 360 degree view of Istanbul, including the entire Sultanahmet peninsula: crowned by Topkapı Palace, the Blue Mosque and Hagia Sophia. A beautiful spot worthy of a lot of pictures. Also houses a restaurant.
İstanbul Modern
A must see for anyone interested in contemporary Turkish art, this is a nice, organized museum with contemporary installations. Including a cafe with a top notch menu and view.
Galata Convent of Whirling Dervishes
A dancing hall of the mystical Mevlevi order, shut down in 1925 along with all other 'reactionary' movements in Turkey. Today the building houses the Museum of Divan Literature. Note: the main hall is closed for restoration through December 2010. The best time to visit is Fridays between 5PM to 7PM when sema dervish ceremonies are staged buy tickets in advance, as space is limited. Also check out the small graveyard next door, where the carved fez perched upon the gravestone indicates the occupant's rank in the dervish hierarchy.
Pera Museum
A private museum with a large painting collection and archaeological collections of measurement units and tools used in Asia Minor since antiquity and faiences of Kütahya.
French Institute
They have good art exhibits for free and sometimes have French films in the cinema.
Hagia Triada Orthodox Church
Finding a quite large and still operating church on the edge of the main square of the largest city of a predominantly Muslim country may not be expected by everyone, but this is exactly the definition of the quite elaborate Hagia Triada.
S. Antonio di Padova Catholic Church
Although not at the size of Hagia Sophia, this is the largest church still used for religious activities in Turkey. Itâs directly on Istiklal St, but somewhat hidden from view by its yard portal. Masses in Italian, Turkish, and English in different days of the week.
Cezayir Street
Better known as Fransız SokaÄı or La Rue Française, i.e. "French Street", is an alley of statues and geraniums hanging from windows, featuring France-themed restaurants, cafes, and pubs housed in renovated and brightly-painted neo-classical buildings. Upon its inauguration in its present form in 2005, there was a brief debate on how political correct it is to rename the street from Cezayir Algeria to Fransız, who fought a bitter war against Algerian independence in 1960s, which led the city council to abandon the idea of officially renaming the street.
Crimean Memorial Church
A neo-gothic anglican cathedral which would not be out of place in northwestern Europe, Crimean Memorial Church was built for the protestant community of the city by Britain in late 1800s. It was named in honour of the soldiers died in Crimean War of 1856, which was fought against Russia by the allied Ottoman and British Empires. Still open for religious purposes, its congregation today mostly consists of Anglican East Asians and Sri Lankans residing in Istanbul.