If you walk along the Danube you'll see a statue overlooking Budapest from the top of a hill. This is the Independence Monument.
The Independence Monument is the towering statue of a woman holding out a palm leaf, to symbolize peace. This was erected in 1945 in honour of the Soviet military who liberated Hungary from facist rule. The statue is lit up in the evenings, and during certain festivals (such as St Stephans Day) fireworks are shot up from above the statue.
You can walk up to the statue by taking various paths up Gellert Hill which lead not only to the Independence Monument but also to the Citadella. It's well worth the trek to the top, as the views of the city are fantastic, and the park land around the hill makes for a nice walk on a sunny day.