In and around Amsterdam, you won't find very impressive nature. For real nature lovers Amsterdam has, like many bigger cities, a botanic garden. You'll find it next to the Zoo (Artis). Hortus is one of the oldest (1638) botanic gardens in the world.
Some numbers about what you'll find behind the 300 year old gates: The garden part has 8000 sorts of plants from all continents. The greenhouses have over 4000 different sorts. A big part of the collection is in Amsterdam thanks to the Dutch East India Company (VOC). Besides getting into history and nature, Hortus is also great for a chill session.
De Hortus is famous for its Cycas Palm collection, from which one is over 300 years old.