Hi there, nice to hear from you,
oh Istanbul!!! Good choice as it is a very nice . destination
Back to your inquiry, 4 days in Istanbul it is just ok, if you know what are going to visit, I mean you have a plan
You can start by the old city Sultanahmet for the 1 day, where are situated the Blue Mosq, Ayasofia museum, 2 day visit Top Kapi Palace (highly recommanded) and in the afternoon Abayzid the great Bazar, 3 day Sulaymaniye mosq, Then you cross the Galata Saray bridge, ask for the fish Market and enjoy fresh fish and on the other side is the European side of Istanbul where are Taksim Square, and Istiklal Kadessi is a street for shopping, having coffe. clubbing, etc...
on the 4th day, you can have a day trip by taking a ferrty to Queen Island, back to the hostel to prepare your stuff to go to Marmaris.
I wish this short answer would be helpful, I am so sorry to reply late as you know I still travelling, at the moment I dont consult messages so often,
Have safe trip and enjoy it
let me know when you back to England, we can meet for a coffee if I am in London