The Thinking Cup is a cafe at Newbury street, in Boston. They serve coffee and scones. The place is usually packed.
At the beginning of the book, Samirah al-Abbas has arranged a meeting with Magnus Chase and Otis at the Thinking Cup. Samirah had to leave to go reap a soul before Otis arrived. Otis showed up in a trenchcoat and ate the scone that Magnus had wanted to save for Sam. They Otis explained that the hammer was still lost, but that he had an idea of where it might be, namely in the barrow of a Wight in Provincetown. Right then, Otis got killed by a mysterious assassin with a wolf-mask, who turned out to be Utgard-Loki later. After the assassin managed to escape Magnus went back to the Thinking Cup
During chapter 56, they meet again.