Plan B: In case of a rainy day, I would suggest to skip the park and head straight to the Royal Academy of Arts, one of my favourite contemporary art museums in London (best show I’ve ever seen was Ai Wei Wei in 2015).
Now it's time for Central London! When exiting in the east of the park you’ll find yourself in Mayfair. For gallery lovers like myself, this is the place to be! From Berkeley Square, to New Bond Street, to Dover street, here you will find the buzzing elite of London, which is especially beautiful in the winter months with all the decorations. (A few of my favourite galleries are Cardi Gallery and Thaddeus Ropac, built in traditional London Townhouses).
I personally prefer the quieter streets of Soho, so after this long walk I would head there for some lunch. Soho is known for it’s small spaces, quick service, and many asian restaurants! My personal favourites are Bao, Koya, and Duck and Waffle (very iconic dish, even better if you have time to go to the one in the Heron Tower). If you happen to be in Soho in the evening you must go to Blanchette! Exquisite French food with a romantic yet upbeat ambience.