Orchards grow so well in climates like Singapore's so it's no surprise that the National Orchid Garden has such a great variety of these beautiful, sometimes curious plants. This garden sits within the Singapore Botanic Garden (free entry) and is surprisingly large with indoor and outdoor gardens including the Cool House (take a breather from the heat here) and the VIP orchard section with unique specimens named after the famous and infamous.
The entry fee is $15 (only $1 if you're local), but with over 1000 species and 2000 hybrids on display, and more being nurtured, (they run a breeding program here too), I think it's well worth the price.