Kew Gardens — the Royal Botanic Gardens — lies just northeast of Richmond and is one of the great botanical collections in the world. The 121-hectare site contains glasshouses, arboreta, formal gardens, and wild areas, all organised around serious scientific work as well as public enjoyment. The Palm House, a massive Victorian iron-and-glass conservatory built in the 1840s, is the most iconic structure and houses tropical plants from across the globe.
Kew is worth a full day, not an hour. The Temperate House (the world's largest surviving Victorian glasshouse), the Japanese Landscape, the Treetop Walkway, and the various specialist gardens each reward time. The best season depends on what you want: the bluebell walk is excellent in April, the roses in June, the autumn colour in October. Entry costs around £20 for adults; it is free for under-16s. It is a 15-minute walk from Richmond along the river, or one stop by tube on the District line.