First time visitors to Budapest and traveling with daughters (19 & 22) at end of May. Aside from the big 'must-see' sites, wondering if any of you have recommendations for neighborhoods in the city that are interesting to just wander, poke around and explore? Or specific cafes worth a stop to people watch and just relax awhile. We'll be staying at a VRBO near the Karolyi Kert park & Petofi Irodelmi Museum (don't know what part of the city that is called).
Also with our limited time, is it worth going for a 1/2 day visit to Szentendre? Or would we find cute areas to see within Budapest?