Any restaurant recommendations for the Mayfair neighborhood?

Not often in that neighborhood when I’m in London so no first hand recommendations. However,
Timeout is always a good resource;
https://www.timeout.com/london/search#/?sort=relevance&q=mayfair%20restaurants&viewstate=list&page_number=1

So are London food blogs:
http://londoneater.com
http://cheesenbiscuits.blogspot.com/?m=1

And from Condé Nast:https://www.cntraveller.com/gallery/best-restaurants-london

I do recall I liked the food at the Guinea. It’s a pub.

Nobu, Park Lane

Le Boudin Blanc in Shepherd Market

The Guinea Grill, Briton Place

The Grazing Goat, New Quebec St

Rowley’s, Jermyn St

There are dozens of good restaurants in this area.

We spent 2 weeks a few blocks away from there last fall. We don't eat very posh and usually we have lunch out more than dinner, but I have a few ideas or you.

If you want a nice pub meal (especially for lunch on Sunday) try The Audley, a 10 minute walk away. Near Marble Arch (not too far) we had a nice Lebanese meal at Maroush Gardens. A 15 minute walk away is The Queen's Head, a gastropub near Piccadilly that we enjoyed very much. They take reservations, which is nice.

It is not in Mayfair but we had great meals at Jamie Oliver in Picadilly--very creative menu.

I don't tend to eat in Mayfair - it is generally significantly over my budget.

Not too far away is Marylebone Lane and St Christopher's Place, both with plenty of restaurants and other eating places.

Take a bit of care if counting on eating at a Jamie Oliver restaurant. They are in a lot of financial trouble, and many have closed. Those remaining still produce good stuff, just be aware that they may exhibit difficulty.

We stayed at the Athenaeum hotel last September and had a terrific stay - make sure to eat breakfast in the hotel at least once! As far as your question, we ate one evening late at the Mayfair Kitchen in the the Mayfair Hotel. We tend to prefer a more casual vibe and this place had a great food/wine and an upscale, casual vibe with good service. We liked it and it is a short walk (about 10 minutes). Give it a try and enjoy your stay.

My favourite restaurant in that area is the 2 Michelin star La Gavroche. Fantastic tasting menu, but if you want the experience without the high prices you could try to get a lunch reservation. The fixed price deal is superb value and includes half a bottle of wine per person and mineral water.