Use 'at that' to stress a point or show that something is notable or unexpected.

Emphasis and Surprise

'At that' can add a feeling of completeness or finality to what you're saying.

Speech Enhancement

It can highlight a contrast or unexpected aspect in relation to the previous statement.

Use 'at that' to refer to a specific place, often just mentioned or known to the listener.

It can clarify or emphasize the exact location you are talking about, especially when there are many options.

This phrase is most appropriate for physical locations, not abstract ideas.