We just came from Antalya and also spent one night in Istanbul though we are going back for moreno our way out of Turkey. Stayed in the Sabah Pension in Antalya and really enjoyed it. Right in the heart of the old city and a great breakfast. We did go to a beach there just by the museum but there was no sand, all rocks and pebbles, but still full of people. Better beaches are outside the city I believe.
In Istanbul we stayed at the Cordial House, near Sultanhamet. It was typical backpacker place. Fairly cheap, breakfast is extra. Not much security for a hostel though, only one key per room.
Have fun! about 7 years ago