Where did Columbus hope to reach by sailing west?

He hoped to reach the Indies (China and India).

Although mariners and cartographers had already accepted that the Earth was round, Columbus was one of the few who believed that he could reach Asia by sailing west across the Atlantic, a voyage most would not have dared at the time. Underestimating the actual distance to China and India in the eastern hemisphere (three times as far as from the Middle East), he thought he had reached the East, and called the natives he found "Indians." Only later did explorers realize that he instead discovered a whole New World, the continents of the Americas.