Right next to Matthias Church, there is a place called Fisherman’s Bastion, one of the favourite places for me when I visited Budapest. A place which we visited twice, once by taking the Funicular to the top of the Buda Castle and the next time taking the blue bus ride which takes you all the points of the Castle District.
However the bus stops after 5 pm so you can later walk down after visiting the castle district. And it’s one of the awesome walks to take. Fisherman’s Bastion built by Frigyes Schulek, who redesigned Matthias Church too. Originally there was a real, grey, lumbering bastion build fishermen took their catch to the fish market next to Matthias Church and protected them during the middle ages.
Today, there is a stone laced fragile looking castle made with marble stairs. When you wander and take pics around you will find a cafe which will provide you with the best view of the Danube river and the parliament.