Hurriyet Daily News is the oldest newspaper in English language. It was founded in 1961. It is owned by Dogan Media Group, a part of Dogan Conglomerate, which is one of the largest corporations in Turkey.
Anatolian Agency is founded by Ataturk in 1920. It's the first and largest state-run news agency of Turkey. Here is the English language section. It only provides daily press scans of the Turkish news.
Bianet is the center-piece of Independent Communication Foundation (IPS). It is an ongoing project with a goal of strengthening the independent media. As a non-profit, it collects donations from local and international resources. It focuses on bringing the unheard voices to everyone's attention.
The Journal of Turkish Weekly is published by an Ankara based think tank, International Strategic Research Organization (USAK), founded in 2004. They focus on regional and international politics.
Sabah is founded in 1985 by Dinc Bilgin, a journalist & businessman. Sabah changed hands in 2008, and was sold to Calik Conglomerate.
Cumhuriyet is founded in 1924 by Yunus Nadi Abalioglu, one of the most reputable journalists in Turkey. Cumhuriyet is owned by Cumhuriyet Association. http://en.cumhuriyet.com/
Today's Zaman is founded in 2007. Hurriyet Daily and Today's Zaman are the most visited English language local papers. It is owned by Feza Gazetecilik and Samanyolu Broadcasting Group. http://www.todayszaman.com/mainAction.action
For food, art, social life, events, you can check also out these magazines: Timeout Istanbul, Guide Istanbul.