Here is my map of some sites visited in the West and South West of Londinium.
The places to the South of the Thames are featured on my www. rurallondonsouthside.com site so nip over there to check them out if you like?
Richmond Park has always been close to my heart. I scattered my Mum's ashes there as it was a place we visited together often when I was a nipper and later with my own sprogs in tow. My Mum Edith loved the park and the Isabella plantation in particular especially in spring when the Azaleas and Rhododendrons are blossoming.
Ian Dury one of the main characters of the Punk period and beyond also enjoyed the park and has a bench dedicated to him by King Harry's mount on the West side of the park.
I could not pick a place other than Richmond Park to recommend above another as they are all so special in their own individual ways, so perhaps buy an Oyster Card or take a stroll and investigate for yourselves and feast on the delights on your doorsteps!
By the way check out Dada records if you like your music as it is a neat store in Chiswick, sells vinyl too if you like that kind of thing, after a strolll around Gunnersbury Triangle perhaps?