prenoćiti

1. to spend the night; to stay overnight
   Prenoćili smo u malom hotelu na Zlatiboru. — We spent the night in a small hotel on Zlatibor.
   Ako je kasno, možeš da prenoćiš kod nas. — If it gets late, you can stay the night at our place.

At someone's place is kod + genitive (prenoćiti kod prijatelja); in a place is u + locative (prenoćiti u hotelu).