South Kensington

Museums- Exhibition Road

Victoria & Albert- 

Obviously, aside from the exhibits in the museum, please, make a point of visiting the café (especially, "The Green Dining Room", designed by William Morris), and the garden

5 Thurloe Square- the so-called "Thin House" (Across the road from V&A museum)

Natural History Museum

Science Museum

Royal Albert Hall (across the road from Kensington Gardens- Albert Memorial)

Imperial College London (behind Royal Albert Hall)- Brian May (Queen) did his Physics degree and PhD there. Beit Hall was the site of Queen's first ever concert. 

More on Queen landmarks in London (many in the area)- link to map

Holland Park- - please do visit Kyoto Garden

Instagrammable spots/eating out: Churchill Arms 

Kynance Mews- very popular among instagrammers, has been a film location in the past (map)