After paying for my visa and entering Turkey, I located the Turkish Airlines Hotel Desk. For passengers connecting in Istanbul, Turkish Airlines offers a choice of either a hotel room or a guided tour of Istanbul, coordinating both offers from the “Hotel Desk.” (Its name is not completely intuitive to its purpose for those looking to take the city tour.)
Since I was interested in taking the city tour the next day, I had made my own hotel arrangements, selecting the Holiday Inn. While it is billed as an airport hotel (and it offers a shuttle), it is about 6 miles from the airport itself.