The Pál-völgyi caves are free with the Budapest Card. Note the caves are closed on Tuesdays. The Buda Hills are the perfect stop for a bike ride, but there are other ways to explore too.
Your "Budapest bucket list" should include the ... Rooms have views of the Danube and the Buda hills, old town, and castle beyond. On a "leafy square" just outside of the Palace District, said ...