The Chain Bridge is the oldest permanent bridge that spans across the Danube to connect Buda and Pest. The bridge is open to traffic and has sidewalks for the pedestrians as well.
Due to its age and beauty, the Chain Bridge is certainly one of the most famous buildings in Budapest and a great photo scene. Especially after sunset, when the lights illuminate the bridge, it is a great sight.
Photo spots can be found on both sides of the Danube. Ideally, you have a tripod with you to take shake-free photos in the low light.
Another tip, if you are on the Pest side (east) go next to the Danube towards the south (towards market hall). After 100-200m you will find the bright Budapest lettering, which looks fantastic within pictures.