As any regular tourist the best way for me to see the river gorge is to queue up for the very popular raft tickets. It will take you through the gorge for about half an hour. On the way you can see beautiful rock formations. The guides don't really speak any English. Some rafts also come from Slovakian side every since they both are part of the EU. You can park your car at the end station of the ride and take a minivan to the ticket booth. There are also two lengths of the ride but the long one is not often available because the best part is actually just after getting on the raft. Keep this in mind for parking the car.

There is also path along the gorge which is popular with bikers and hikers. It will take you a few hours but should be as enjoyable as the ride.