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Many people who come to Japan from European countries say that they wish they could stay here for ever.
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Many people who come to Japan from European countries say that they wish they could stay here forever.

This is fine.

Comments  
teacherJapan Many people who come to Japan from European countries say that they wish they could stay here for ever.

forever

"Come to" has some implication that they already intend to stay. "Visit" eliminates that slight problem: "Many people who visit Japan from European countries say that they wish they could stay here forever."

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 Clive's reply was promoted to an answer.
Thank you so much for your help, Clive and anonymous.