Listed below are some of the must-see sites for any first-time visitor to Istanbul.

Blue Mosque (Sultan Ahmet Mosque) . It is one of the most famous monuments in both the Turkish and Islamic worlds. Its six towering minarets and vast main chamber are highlights. Visitors are allowed except during prayer times.

Hagia Sophia. The Hagia Sophia Church was re-built in the 6th century by the Emperor Justinian on the foundations of a previous church bearing the same name which was destroyed. It was one of the largest basilicas in the Christian world until the Ottoman conquest of Turkey, when it was converted to a mosque. Today it houses a museum, but far more interesting than any exhibit is the building itself. 

Topkapi Palace.

Grand Bazaar. You can spend hours wandering from stall to stall in the covered Grand Bazaar market. Even if you have no interest in shopping, you will thoroughly enjoy the spectacle and atmosphere of this ancient marketplace.

Istanbul Modern.  Housed in a renovated warehouse on the Bosporus (next to the cruise ship terminal), this museum / gallery features works by a variety of Turkish artists  from the 1800's to present day. There's a nice gift store, and a delightful café overlooking the water.

Sadberk Hanim Museum. This is a small museum exhibiting the private collection of the Koç family, one of the wealthiest families in the country. It's really two museums in one. One half (Art History) is housed in a restored Ottoman mansion. Its three floors hold a sumptuous collection of Islamic art, tapestries, calligraphy, Ottoman costumes, artifacts, and furnishings. The second half  (Archeological) is next door in a modern purpose-built building. The collection includes artifacts from Roman, Byzantine, and Hellenic times, some dating back to 5 BC. 

It is easy to be intimidated by Istanbul, especially if this is your first visit to a Muslim country. However Turkey in general, and Istanbul in particular, is incredibly welcoming to foreigners. The very helpful and friendly Tourist Police in Istanbul do a good job keeping travelers safe. First-time visitors can arrange guides upon arrival from a variety of outlets, or organize sightseeing to the Blue Mosque and St Sophia ahead of time.