The phrase "first place in my heart" is perfectly correct. It sounds tender and sweet. Here are three examples: A religious person might say, "God has first place in my heart." A man says, "Of course my career is important to me, but my family has first place in my heart." A traveler remarks, "Of all the countries I have visited, Italy has first place in my heart."

It sounds ok to me,not like a Native speaker but I can't think of another expression for that.