1 "came into my mind"= a thought or idea came into your mind. 2 "come to mind" = you can also use this to say you are going to care for someone/something 3 "it entered my mind" = same as 1 4 "it crossed my mind" = similar to 3 a thought/idea entered your mind you didn't think about it very seriously you considered it "come to think about it" = a common natural way you are thinking about it, use this instead of 2 to avoid confusion. "come to think about it, I think that's a good idea" "it crossed my mind to go visit my Aunt today" "it entered my mind to jet off on holiday" "A bad thought just came into my mind" "I came round to mind your garden" = you came to care/tend their garden, look after, watch over They are sometimes interchangeable, although there is sometimes subtle differences in their use. "come to mind" when saying a thought suddenly came to you. We usually say it at the end of the phrase or sentence. ( -------- -------- + nothing comes to mind right now) examples of using it this way. https://idioms.thefreedictionary.com/come+to+mind

We have an idiomatic expression which we use - 'come to mind'. It is best to use this one. Some of the others are not grammatically incorrect, but if you want to sound natural, then do use that expression.