Istanbul International airport to Inter-Continental by taxi should be about $10 as advised, and 30 minutes to an hour with traffic. I stayed at the I-C in October and traveled extensively throughout the city by taxi without difficulty. Fares are very low by USA/W Europe standards, and taxis are found in great abundance at the major hotels and tourist spots.
One pays the visa fee BEFORE the arrivals hall. They handed me a sticker to place in my passport. It's US cash, correct change appreciated, in what might have been described as a scrum, not a line, when I passed through.
The advice on TKL currency given above is good. Problems arise when the posted price isn't obvious - did they truncate 2 zeros, 3 zeros, or more? Prices for everyday items are really low (and that observation from October was at 1$US = 680,000 TKL), so stock up on small bills.
Try for a Bosphorus view room and enjoy your trip.
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