Istanbul
Istanbul is strategically located on the Bosphorus and is split between Europe and Asia. It truly is a city where east meets west. Istanbul is the cultural and financial hub of Turkey, and also the most populous city. The sites are countless and there's something for everybody, whether you're interested in art, music, food, or adventure.
The must see sights include the Blue Mosque, the Hagia Sophia, and Topkapi Palace. Also be sure and take in a show of the famous Whirling Dervishes. Istanbul is also a wonderful city to explore by simply wandering through its many diverse neighborhoods. You can pass many days explore both the residential and commercial pockets of this city. Much of the appeal is hidden away along back alleys or within corner shops.
The Grand Bazaar is a great place to shop. It has an interesting atmosphere, and although it is definitely touristy, you can still find sections that cater to local Istanbul residents. It's a fun place to try your hand at bartering and most shopkeepers are lighthearted and keep it fun. Look at it as a game, and you'll enjoy it all the more. The spice market is a smaller version of the Grand Bazaar, but it has more spices and foods. It's also a great place to pick up the famous Turkish Delight.
Transportation in Istanbul can be chaotic, but is generally readily available. There's a convenient tram system, many buses, and subway, and ferry that you can use to cross the waterways. Be sure and hope on a public ferry (at Eminonu) to head to some of the suburbs along the Bosphorus including Uskudar and Besiktas and Kabatas.
You'll find a large number and diversity of restaurants around the city. The costs range from budget to extremely high end and they all have something fun to offer. Also make sure you try some of the great dessert cafes that are ubiquitous around town. The prices are quite cheap and the desserts are delicious. Some even offer rooftop views of the Blue Mosque, so they're a great place to visit at night when the city is lit up.