When the weather is nice the boat rental on the Rursee with paddle boats and canoes is great. Bicycles with child seats or child trailers can also be rented there, and the natural outdoor pool Einruhr or Rurberg provides the necessary cooling afterwards:
The swimming pools of the region are ideal for small water babies:
You can perfectly watch animals in Euregio zoo in Aachen, in GaiaZoo in the Netherlands, in the game enclosure Hellenthal with an impressive bird of prey show and during a small walk in the game park Schmidt.
A different way of watching animals and independent of weather can be experienced with all senses in the really awesome exhibition "Wildnis(t)räume" in Vogelsang and in the adventure museum "Lernort Natur" in Monschau.
There are a variety of amusement parks, for example the "world walk" in Mondo Verde, inexpensively in De Valkenier and unforgettably in Phantasialand Cologne.
Living history can be found at the events at Satzvey Castle, e.g. the Knights' Games, and in the open-air museum in Kommern.