The correct phrase is "Are you open today?" This is because the word "open" is being used as an adjective to describe the state of a business or establishment. In contrast, "Do you open today?" would typically be used to inquire about the specific action of opening something, rather than the general operational status of a business.
Related Q&A：
Is it correct to say are you open today OR Do you open today？-Well, neither of those is exactly perfect. The more common and correct way to ask would be \Are you open today?\ That's the phrase you're most likely to hear in normal conversation. \Do you open today?\ just doesn't sound quite right. It's a bit off. But if you were to say it, people would probably still understand what you mean. So, if you want to be sure you're saying it the usual way, go with \Are you open today?\ Oh, and that's how we do it in American English!
