This place has some really nice bridges that remind me a little of paintings by Monet. It also has a bunch of really nice, big rhododendron bushes!
That being said, Trompenburg Arboretum has a really nice variety of different trees, shrubs and bulbs so that there is something to see in every season. There are 700 different kinds of rhododendrons which bloom from March through August, over 250 kinds of oak, 7 kinds of beech and southern beech (among them Nothofagus antarctica), about 100 types of holly and a nice collection of cacti in the greenhouse. In addition, there is a decent collection of about 500 hostas (plantain lilies) which is part of the National Hosta Collection.
Even though it is located in a busy city, it still feels like a tranquil place to spend time in.
With a little luck, you will also find a couple of Egyptian geese, (and maybe even with goslings) roaming around the park and swimming in the ponds and ditches nearby. With strikingly dark circles around their eyes, they are easy to recognize. Egyptians considered them sacred and they've been adorning the Dutch landscape for the last few years now although they are considered exotic.
You can find more information here; This is the English page but information is scarce. If you like, check out the home page; you may not be able to read the texts but the images are well worth it. In addition, they have a Facebook page, and that contains many more beautiful pictures.