Just as the most natural-sounding English sentence using your set of sentence options: "Tell me the date" is correct. However, I agree with Paul: if you're asking for today's date "What's the date?" or "What's the date today?" is preferred.
If you're asking about a specific event, it's probably more common to just ask "When is it?"
Example:
"You should come to the staff party."
"I'd love to. When is it?"