Is it correct to say "I hope you have a good day"? Is there a better phrasing?

Good question! The answer is actually a bit more complicated than you might think, but hopefully will help you understand a bit more about when to use certain tenses. "I hope you have a great day." is a fine sentence. An even better sentence would be "Have a great day." without "I hope you". Why? In English, commands, or the imperative tense, is can sometimes be considered rude. In more formal settings, we say "please pass the butter" instead of "pass the butter", "can you do me a favor" instead of "do me a favor", etc. But these are examples of when you are telling other people to do something for you. What if you are saying something just to show other people you care about them? In this case, it's fine to use the imperative. "Have a great day" and "Enjoy your meal" are two examples.