Love Hina Spring Special (2001)

Keitaro fell asleep during his Tokyo U exam. He was so embarrassed that he was going to fail a fourth time, that he runs away from home, visiting a far away island instead. Naru decides to go after him, and worried, their friends visit the island as well. When Naru gets there, she sees Keitaro, but he's running away with another girl. Naru has to figure out what's going on, and their friends have to try not to stay lost.