On a budget, Kew Gardens (Royal Botanic Gardens) still earns its price.
£22 (cheaper online/off-peak)
300 acres of plants, palm houses and a canopy walkway — a serene escape from central London and stunning in spring and autumn. The catch: it's in zone-3 southwest London (30–40 min out), the ticket isn't cheap, and you need half a day to make the trip worth it.