I took a punt that the OP was a first time visitor based on the fact that he was looking for a safe means of transport (a repeat visitor would not be concerned); would consider a subway (IST isn't served by one); and didn't know how much a taxi might cost. I took a further punt that he was likely to be a tourist given that he was concerned about cost (hence not travelling on company expenses) and arriving on a Friday evening. Obviously he might be a party animal looking for the nightclubs around Ortakoy; he might be looking for a suite at the Four Seasons, but I just guessed that wherever he stayed, he might end up losing half his time and all of his wallet in taxis between the Conrad and Sultanahmet.