I will never forget the day when I first met you on the ship.正确

I will never forget the day on which I first met you on the ship.正确

当定语从句既可以用when也可以用介词+which引导时，用when更简洁，用介词+which显得很正式。日常英语首选when, 很正式的语体用介词+which。二者虽然意义相同，但语体风格不同，应根据需要使用，而不是任意的。

I will never forget the day on which time I first met you on the ship.错误

既然用介词on, which则指代the day, time属于多余。因此on which time=on the day time属于结构错误。