Take the chair lift (up 400+ ft.)above the castle. The views of the river and the town spread out below the castle in a semi circle are breathtaking. The walk down to the castle isn't too bad but the trail through the forest can be a bit slippery so have good tread on your shoes. The castle reminds me of a fairy tale - it is surrounded by green forest and I was expecting to see knights & fair maidens - but I guess they were hiding somewhere. Walking back to town from the castle is easy. You could also walk up to the castle if you're not big on chair lifts but the walk up is a bit steep.
There is a museum dedicated to Victor Hugo (he lived here during his exile) but I didn't have a chance to visit it.
Quick Tips:
There are well maintained and signposted hiking trails around Vianden so plan to spend the whole day. If you'd like a longer visit, there is a hostel & other accommodation as well as lots of restaurants & cafes.
There are no taxis in town - when I enquired about renting one I was told they'd have to radio one in from another town & I'd be charged for the trip from the other location.
Best Way To Get Around:
Vianden is very small so walking is the best way to see it. To get to Vianden from Luxembourg City on public transportation, you need to take a train & then a bus. The easiest way to get there is by car.