Hotel lobby/coffee shop near Lincoln’s Inn

[Pottedpalm]

Am meeting daughter and young baby at Lincoln’s Inn while her partner has a meeting there for a couple of hours. I’m thinking that a smart hotel lobby/coffeeshop might might be quieter and less crowded than a normal coffee shop. Any ideas? It is a while since trips to London were a weekly event and Im a bit out of touch!
Also if anyone has a suggestion of a good eatery for after the (daytime) meeting, preferably a reasonable stroll away, please share.
thank you!

https://themcr.lincolnsinn.org.uk

https://www.peartreecafe.co.uk/lincolns-inn-fields
https://www.rosewoodhotels.com/en/london
https://thehoxton.com/london/holborn/

The above would be for coffee. Restaurant-wise, you're on the edge of Covent Garden with Mayfair, Soho, and the South Bank beyond if you're up for a stroll, so you'll need to be a lot more specific about about you like/want!

Thank you so much for suggestions.
@TheOccupier The Hoxton looks as if it would be ideal for hanging out. I’m less worried about the restaurant for later, I realise there is a great deal
of choice!