Kilkenny city centre is small enough to walk comfortably. The main axis of the Medieval Mile from the castle to St Canice's Cathedral is about a kilometre and takes 15–20 minutes at a stroll. Everything of interest in the centre is within 10 minutes' walk of the castle.
For outlying sites — Dunmore Cave, Jerpoint Abbey — you will need a car or a taxi. Local taxi firms are readily available from the city centre.