A short bus or combo train/bus ride will take you to Clervaux from Vianden. As well as a 12th century castle, there is a large twin spired church and a Franciscan monastery on the hill above town.
Although a bit steep, the walk to the monastery is enjoyable as you get great views over the town. There is a well stocked gift shop selling lots of regligious articles in the monastery. As well, it's possible to attend a concert to hear the chanting of the monks - supposedly they are well known throughout Europe. You would need to enquire in advance re: dates for this.
I didn't find Clervaux castle as interesting as the one in Vianden because there were only a few areas open to the public. The Family of Man photo exhibit at the castle is a compilation of pictures of people taken in the 1950s from around the world and is worth a visit. There are also two museums housed at the castle-one dedicated to the military and another with models of ancient Luxembourg castles. Each of these three areas have separate entry fees although they are free with the Luxembourg tourist card that you can get at the Tourist Information Centre. Otherwise, the cost is only a few dollars.
Clervaux isn't as compact as Vianden (the train & bus station is about a 10 min. walk from the centre of town) but was still worth a visit. There were a number of outdoor cafes and restaurants where you could stop for a drink or have a meal.
From Luxembourg City, a direct train to Clervaux takes about 1 hour.