When in London, this one can't be missed. Slightly out of the center, it is reached easily by public transport. Depending on where you're based, the Kew Gardens and the Richmond train stations are probably your best stops. From there it's a short walk with signs directing you to the nearest entrance (yes there are multiple).
The site itself is huge. Climbing the pagoda was fun, especially the short explanation on how the gardens were used to test smoke curtains in Second World War was impressive. If you really want to see, read and do all things, you probably won't be able to do that in one day. On 'good days' some of the places can get a little crowded. At 25 GBP the entrance fee is a little steep, but this is kind of the norm in England.
The value for humanity is explained throughout the site, with many plant, seed, fungus and other signs and descriptions explaining why their work on them is important for our understanding and their survival.