Buda is the green lung of Budapest, in my opinion. I enjoyed living there, especially for this reason. When I lived near Gellert hill I liked discovering green areas nearby, and the most peculiar is the Arboretum, one of the few organized green spaces with a wide diversity of plant species.
When I moved to Budapest it was disappointing to find out that it does not have a huge botanical garden but several smaller ones. I consider the Arboretum as such. It has everything a typical botanical garden has: various species of plants (mainly trees), a small greenhouse (closed to the public), an edible plant section, and a pond. No wonder, as the Arboretum is right next to the Horticulture University and the students can practice right away.
Unlike other parks, this one does not have big crowds or any sort of entertainment that would ruin your unity with nature. Here you can really enjoy bird watching (or at least you can hear them), space and the absence of loud crowds. The place was recognized as a bird-friendly one in 2006.
If you love nature and want to be away from civilization but still close to the city center, visit a protected nature area, meet birds, or study plants, Arboretum is an ideal place for you.