In "New Moon," after Edward Cullen realizes that Bella is in danger due to a paper cut that causes Jasper to lose control, he decides to end their relationship to protect her. Subsequently, the Cullen family leaves the town of Forks, Washington

. The Cullens relocate to Ithaca, New York, where they take up their various pursuits

. Edward initially joins his family there for a short time but then leaves to pursue Victoria, the vampiress who threatens Bella. Edward travels south, eventually reaching Rio de Janeiro, Brazil, where he tracks Victoria and even calls Bella from there

. Meanwhile, the rest of the Cullen family remains in Ithaca. Later, they also make a trip to Alaska to visit the Denali coven, though that detail is less certain in canon

. So, in summary:

• The Cullens move from Forks to Ithaca, New York.
• Edward leaves Ithaca to hunt Victoria, traveling as far as Brazil.
• The rest of the family stays in Ithaca during Edward's absence.