Boeing737sr
In Istanbul on the Asian side I would recommend the area close to bagdat street and Bostanci. It's a street full of restaurants and a some bars. You also have a long asphalted sea walk if you feel you need to exercise.
From here you can easily take a small mini bus (dolmus) to Taksim (city center) or several other places. It's also close to the sea bus station: Bostanci, from where you can go to the European side and Ataturk airport (IST) without being bother by the infamous Istanbul traffic.
You will be f***ed by the price if you come as yabanci to look for a flat, and not many agency speak English. Ask someone from pegasus office to help you. If they can't help you I have a number to an English speaking guy.
Take a flat without furniture and buy new stuff at IKEA. Because the one with furniture are often way more expensive and the standard of the furniture are often very low.