Use к + Dative and у + Genitive for 'to' and 'at' people's places, respectively.
The preposition у generally means 'by, near, at' and can be used very much like French chez: у Петрђ 'at Peter's place, chez Pierre'. This expression refers to any place normally associated with the person, e.g. their home, office, and so on. Don't use the word for 'house' to say 'at somebody's house' — just use the preposition у plus their name.
У нђс икрђ не ћчень хорћшая. In our country/store/city the caviar isn't very good.
Гдљ Натђша? — У Мђши. Where's Natasha? — At Masha's.
Онќ жќли у негћ. They lived at his place.
It is grammatically correct to use a possessive with somebody's place, e.g. Ћн пошёл в кабинљт профљссора 'He went to the professor's office', but it is better to use two prepositional phrases, one with each noun: к профљссору в кабинљт.
Ћн пошёл к немџ в кабинљт. He went to his (somebody else's) office.
Ћн пошёл к себљ в кабинљт. He went to his (his own) office.
Ћн у себї в кабинљте. He's in his (his own) office.
Чтћ у вђс в рукљ? What's in your hand?