We started out at the lánchíd (chain bridge), the most famous of the bridges spanning the Duna (Danube). From there, we took the sikló, a cable car up the hill that takes you up the incline to the castle. This gives you more sights of the river and Parliament (see pictures below).
At the top of the hill, you can wander by the castle (where there seem to be festivals outside every weekend). When we went there was a festival with music and lots of food and wine.