The Augustusburg was simply an amazing castle, with elaborate design and lavish furnishing. Even though much of the furniture were not the original, it was still a beautifully restored castle.
It is easy to get to Augustusburg because it is just a few hundred metres away from the Bruhl station. The combination ticket, along with the Falkenlust cost 7 euros. To visit the Augustusburg, a guided tour is compulsory for any entry. Guide only speaks German but there are audio guides in various languages. However, German listeners get to enjoy a deeper and more interesting tour.
Falkenlust is a good 2 miles away or almost an hour walk. The distance seems to be longer than it sounds, after passing through the gardens, forest walk and passing through some farmland. Care has to be taken because no clear signage is available and it is not clearly marked on the google map, except for the path Falkenluster Allee for some clues. Otherwise, ask some of the park strollers passing along. No direct transportation, except maybe taxis, is available, which is quite disappointing.
From here, another half day trip can be taken to visit the nearby Aachen Cathedral, by changing trains in Cologne. For the following day, half a day trip up north to Zollverin Coal Mine at Essen can be taken. Probably take Cologne as the base, and for two nights, including the Cologne Cathedral, 4 amazing and quite different world heritage sites can be visited. Do get the regional train pass if traveling in a group of 2 or more. Totally worth it and affordable.