2 Rewrote to be clearer
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So you have two choices:

Not after midnight.
Not until midnight.

After: later than something; following something in time
Until : up to the point in time or the event mentioned

If I asked you, "When did you get home?" you wouldn't say "Not after 2 AM" because that meansafter", you are saying that the restaurant doesn't close later than midnight. It could close any time before midnight, so you did not come home after 2 AMhaven't answered the question "What time does the restaurant close?". You would say instead, "After 2 AMhave said when it doesn't close." 

If you say "Not until 2 AM"until", it means that you were out late and you didn't makeare saying that the restaurant doesn't close up to the time of midnight, then at midnight, it home until 2 AMcloses. That does answer the question "What time does the restaurant close?".

So you have two choices:

Not after midnight.
Not until midnight.

If I asked you, "When did you get home?" you wouldn't say "Not after 2 AM" because that means that you did not come home after 2 AM. You would say instead, "After 2 AM." If you say "Not until 2 AM", it means that you were out late and you didn't make it home until 2 AM.

So you have two choices:

Not after midnight.
Not until midnight.

After: later than something; following something in time
Until : up to the point in time or the event mentioned

If you say "Not after", you are saying that the restaurant doesn't close later than midnight. It could close any time before midnight, so you haven't answered the question "What time does the restaurant close?". You have said when it doesn't close. 

If you say "Not until", you are saying that the restaurant doesn't close up to the time of midnight, then at midnight, it closes. That does answer the question "What time does the restaurant close?".

1
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So you have two choices:

Not after midnight.
Not until midnight.

If I asked you, "When did you get home?" you wouldn't say "Not after 2 AM" because that means that you did not come home after 2 AM. You would say instead, "After 2 AM." If you say "Not until 2 AM", it means that you were out late and you didn't make it home until 2 AM.