This is the Skywalk at the Grand Canyon. This was in the beginning of the book and marked the start of Leo, Piper, and Jason's quest.
After leaving the Grand Canyon with Annabeth, Leo,Piper, and Jason all got taken to Camp Half-Blood where they would live and find out who their parents are.
This is Boreas' Palace, where the three heros visited on their quest. There the met Boreas, Khione, Cal, and Zethes. Boreas sent them out to find Aeoleous god of wind..
This is the city of Chicago where Piper, Leo, and Jason met and fough Medea in her department store, during this part of the story Medea was charmspeaking the boys, Piper freed them of this then they fought Medea, and destroyed her department store.
When they found Midas, Festus crashed and got destroyed. Also, in Midas' home Leo, and Piper got turned into gold, but Jason saved them and when he did they got right out of there.
Enceladus held Piper's father captive throughout most of their quest. When they found him, they all fought, but in the end they saved Piper's father.
Everyone then returned to camp Half-Blood where they were told that was only the beginning of their journey, and that there is a lot more to come. This then signifighed the end of the book.