The correct option is 'c) his place'.
Translation:
Джон пригласил нас к себе.
Explanation:
The sentence requires a possessive noun phrase indicating where John is inviting them. 'His place' means John's home or location, which fits the context of an invitation. 'Him' is a pronoun, and 'his' is a possessive adjective, neither of which work to complete the sentence grammatically.