I left my husband in a situation where "the grass looked greener on the other side" situation. My husband was not a Christian. The man I'm now with is a Christian and treats me much better than my husband did. This being said, is it still wrong to even date this new man? Even if we never get married?
It doesn't matter that your ex-husband wasn't a Christian. It was you, who claimed to be a Christian, who left him.
"Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife" (I Corinthians 7:10-11).
"And this is the second thing you do: You cover the altar of the LORD with tears, With weeping and crying; so He does not regard the offering anymore, nor receive it with goodwill from your hands. Yet you say, "For what reason?" Because the LORD has been witness between you and the wife of your youth, with whom you have dealt treacherously; yet she is your companion and your wife by covenant. But did He not make them one, having a remnant of the Spirit? And why one? He seeks godly offspring. Therefore take heed to your spirit, and let none deal treacherously with the wife of his youth. "For the LORD God of Israel says that He hates divorce, for it covers one's garment with violence," says the LORD of hosts. "Therefore take heed to your spirit, that you do not deal treacherously."" (Malachi 2:13-16).
You left your husband when you had not business doing so. You are not eligible to marry again. To date this man is to give him false hopes. He needs to find a woman he can marry.