West of the river is the Castle District atop of a hill which is stuffed with stunning architecture, a palace, museums and fabulous views. Outside of the castle area by the Danube is the district known as Vizivaros.
Chain Bridge at night… 
and by day.
Walking across the Chain Bridge over the Danube is a lovely way to approach Castle Hill. You can then walk up the Hill or take the Siklo [Funicular], the lazy way.
Fishermen’s Bastion
Once you are at the top and start to wander around you are greeted with a myriad of amazing architecture and views. Fishermen’s Bastion [Halaszbastya] looks like you have entered a fairy tale world of castles, spires and turrets.
Built in 1905 it is not as old as it looks but is impressive nontheless.
Not only are there amazing views of the city and the Danube with its bridges and Parliament building on the Pest side but visible in the distance is the enormous Liberty Monument on Gellert Hill. The monument, erected in 1947, is a tribute to the Soviet soldiers who died liberating Budapest at the end of the Second World war.
The Royal Palace is where you will find the Hungarian National Gallery and the Budapest History Museum for which you will need to buy tickets.
The statues, views and architecture are all free of course. Wandering around the palace grounds is an absolute delight.
King Saint Stephen – Hungary’s Patron Saint.
Matthias Church
The intricate spire and colourful tiled roof is absolutely stunning.
The [mostly] 19th Century church which has been restored at huge expense is beautiful inside and out.
Under Castle Hill
Underneath Castle Hill is Buda Castle Labrynth which has displays showing how the caves have been used since prehistoric days. The Hospital in the Rock is a guided tour through a cold war nuclear bunker used in the Second World War and during the uprising in 1956. Both are fascinating and I recommend a visit, [sorry about the lack of photos].
Vizivaros
Hugging the bottom of Castle Hill with the Danube on the other side is the area known as Vizivaros. It has some attractive streets and squares as well as the ancient Kiraly Turkish Baths.
I was determined to find the Medieval Iron Stump where merchants would hammer a nail to mark their visit. It took some time but I eventually found it, much to Leashia’s relief.
Maria Statue in Maria Square. 
The twin towers of the 18th Century Church of St Anne are striking and the baroque decor inside is apparently also striking but we were sadly too late to venture inside. The 18th Century Chapel of St Florian looks stark in comparison.
Church of St Anne. 
Chapel of St Florian
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