Müngstener Brücke and Schloss Burg are good places to visit if you are staying in Cologne or Düsseldorf.
Müngstener Brücke can be reached using public transport; take the train to Solingen Schaberg or the bus from Remscheid and Solingen. If you are arriving via car there is a carpark nearby along the River Wupper.
Beside Müngstener Brücke being a famous sight in the area, it's also a place that offers good walking paths.
My advice though would be not to do a circular route but to instead walk to Schloss Burg and use a shuttle bus to come back to your starting point. The walk to the castle is a nice and easy walk along the valley and it ends with a steep winding path from the village below Burg to the castle. There's also a chair lift in the valley if you feel too tired for a climb.
The castle itself is used as a regional cultural centre and is worth a visit, as it has both a permanent exhibition and exhibitions that regularly change. There are a lot of little individual shops around the castle as well as many restaurants where you can enjoy a good meal made up of specialities from the area (such as waffles and the Burger Brezel).
If you're too tired to walk back to your starting point, you can catch the hourly shuttle bus to take you back to the starting point at the Müngstener Brücke. All of this can be done in one afternoon or you can make it into a full day trip.
If you're keen on canoing then you can also hire canoes (must be hired in advance - addresses can be found on the internet). The river does not give you a canoeing challenge, but a very pleasant outdoor activity (also great for families) in splendid nature. This option is definitely a full day outing.