I'm not the biggest fan of Budapest, and when I happened to be there on an exceptionally hot Saturday, my desire to leave the city as soon as possible has won over my internal urban explorer. I had a few day trip ideas, but I just went for the easiest one after all. In my defense, I traveled all night to get to Hungary from Armenia.
So, I went to Szentendre and it was perfect. Well, a riverside town that used to be an art colony must be perfect. And it has a huge Open Air Museum that gives a visitor a perfect insight into rural Hungarian architecture. Also, it is really easily accessible from Budapest by both river and rails.
Long story short, just go there while in Budapest.