I consulted TripAdvisor to answer my weekly "What should I do?" (see my Oriental Institute review) question. The conservatory sounded like a good bet, especially since it's easy to get to by train. What an experience!
I enjoyed everything. The Palm House is the first thing you'll encounter and it starts the visit off with a bang. From there, it's on to the Fern House, or wherever. The collection is immense and the building itself is "old school" stunning. I particularly liked the inscriptions and artwork interspersed among the plants. The outdoor exhibits are also nice, but seem to be a work in progress as you venture further from the building, unless that's intentional.
It's hard to say how much time to spend. I was there something over three hours, probably overlooking most of the collection. Even spent time feeding the fish in the Aroid House after an employee gave me fish food.
Probably stating the obvious, but it's very hot and humid in a greenhouse. The floor is sometimes wet and it is intentionally discontinuous in the Fern House. You need to be constantly aware of what's around, and particularly, behind you because some of it is very sharp and pointy. Even some ferns. Oh, and the roof leaks during hard rain. Not sure if that's due to temporary repairs from the hail damage, but there's potential to damage your camera, etc.
The neighborhood is OK during the day. I think.