There are some common questions you can ask if you want to know what the date is.
What is the date?
What is the date today?
What's today's date?
Could you please tell me what today's date is?
The following questions may be asked if someone would like to know about the date of a specific event. A party, an appointment etc.
What date do you fly to Canberra?
When is your appointment?
What date is your wedding?
When is your birthday?
We can use what or when to ask about a specific occasion or event.