Now that I got a moment, time to lay out some analysis.
Key points:
-Qi's security - She's gotten through the tribulation and found her new balance point, but this is still new, and so still something to look out for.
-Chaperone - Are there people around?
-Public perception - Who will see, what will they think?
-Qi's interest level - How interested is Qi in the discussion topic?
-Meng Dan's interest level - How interested is Meng Dan in the discussion topic?
[ ] They were just taking lunch at the main embassy.
-Qi's security - Its a public working space and all. Good for safety, not good for actually talking in depth on anything private.
-Chaperone - Its a public space, there will be people.
-Public perception - A lot would see, but its not really going to stick out as a date unless you're specifically looking for such.
-Qi's interest level - Presumably discussion would revolve around work and politics? Not too thrilling.
-Meng Dan's interest level - Past experience says he's fairly invested in his political cause, but unclear beyond that.
[ ] They were taking dinner in the observatory gardens.
-Qi's security - This is fine, Meng Dan literally already had invited us to a similar meeting back in Xiangmen.
-Chaperone - There are people around, though not necessarily right there.
-Public perception - Not as many people will see, mainly observatory(and thus either Meng or Southern folks) staff, but its a more personal setting, so more stray thoughts.
-Qi's interest level - This is likely to focus around the higher metaphysics of what the Observatory is studying, which leads back into cultivation. As we've previously seen, cultivation esoterica is one of the few topics Qi is usually quite enthusiastic to talk about(at least barring Suyin and Xuan Shi going into full gear at which point they leave her in the dust), especially when the observatory focuses on the visible portions of the Liminal, Sun, Moon and Stellar Qi.
-Meng Dan's interest level - The guy is here
at all because Qi drops Deep Lore out of nowhere. He's probably hoping for more
[ ] They would be having tea in a private coach on the way back to White Cloud Town.
-Qi's security - Its about as private as she's ever been with anyone who wasn't Renxiang, Meizhen or family. How well she adjusts to this may vary.
-Chaperone - Qi thinks they are, because Sixiang and Yinhui are there. Many others would not consider two spirits to be suitable chaperones.
-Public perception - Nobody's going to see anything except at pick up and arrival, but what they do see is going to merit a lot more gossip.
-Qi's interest level - Nothing immediately apparent, could talk about anything.
-Meng Dan's interest level - Nothing immediately apparent, could talk about anything.