Is there availability on [date]?

Meaning

Are there any rooms or tables free on that date?

Examples

• John: <b>Is there availability on</b> October 27th?
• Alice: Let me check... Yes, we have a few rooms available.
• John: Great! <b>Is there availability on</b> October 27th for a party of six?
• Alice: Yes, we can accommodate a party of six on that date.