All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm in accepting the invitation of a non-Muslim especially if he is expected to become a Muslim or in order to repel his harm. Imaam Ahmad reported that Anas narrated that the Prophet was invited by a Jew to eat barley bread with lamb fat and tail fat, and he accepted his invitation. So it is permissible (to accept an invitation) if we assume that the place is free from prohibitions. However, if the place includes some prohibitions like music or women who are not wearing Hijab and other prohibitions, then it is not permissible to accept the invitation. You have to know that Muslims should deal with non-Muslims according to Islamic requirements; it is not permissible to befriend them, or mix with them to an extent to consider them as friends. Allaah says (interpretation of meaning): {O you who believe! Take not the Jews and the Christians as friends or allies.}[5:51]. Allaah also says (interpretation of meaning): {And those who disbelieve are allies to one another.}[8:73]. Moreover, the Prophet said: "Whoever, socializes with a non-Muslim and lives with him is like him." [Abu Daawood]. So if a non-Muslim invites a Muslim and the latter accepts his invitation according to Islaamic requirements which we have previously stated, he has to seize this occasion and call this non-Muslim to Islam. He has to introduce Islaam to him in an appropriate manner so that Allaah may guide the non-Muslim to Islaam because of him. The Prophet said: "I swear by Allah! If Allah guides one single man (to Islaam) by your efforts, that will be better for you than possessing a whole lot of red camels (a very expensive breed of camels)." [Al-Bukhari and others]
Allaah knows best.