The Castle District in Buda, or is it Pest?

Our first full day dawned chilly & foggy. We had a bus tour around the Pest area of the city (Or is it Buda?). We passed by Hero's Square, filled with monuments to Hungarian heroes, and one of their famous and beautiful spas, before we crossed the Chain Bridge, across the Danube, up the hill to the Castle District. We had a short walking tour, followed by free time. A highlight for me was two young men that had birds of prey (A Peregrine Falcon and  a Golden Eagle) that for a price, 5 euro for the Falcon, 8 euro for the eagle you could have your photo (Your camera) taken holding the bird.