Városliget, otherwise known as City Park, was the main venue for the 1896 Millennium celebration, where Hungary’s 1,000 year anniversary was celebrated, thus it holds an abundance of monuments that celebrates Hungarian history. It is one of the most popular public parks in Budapest where many go to relax and enjoy the sun. Almost half the 100 hectare park is luscious green parkland, making it an idyllic spot for picnickers. Varosliget, although a great place year round, really shines during the summer: there are deck chairs around the park, playgrounds for the kids, historical monuments, lakes where you can feed ducks or go for a boat ride, open picnic spaces, and many pedestrian walkways covered by trees providing a refreshing shade during hot summer days. If we had to choose one spot for a picnic, however, we would choose the Kiraly Domb(hill) next to the Millenium Café. This space is a wonderful spot for a picnic as it has lots of trees, beautiful views, and a small hill to fly kites from. Városliget has a bit of everything making it a perfect spot for a picnic as it offers many different attractions but also allows for visitors to just enjoy a bit of nature all the while being in the heart of Budapest surrounded by 1,000 plus years of Hungarian history.
Other attractions in the park includes the Budapest Zoo with stunning turn-of-the-centrury architecture, the Municipal Grand circus, the Széchenyi Medicinal Baths, Vajdahunyad Castle, Hero's Square, the Museum of Fine Art, the Palace of Art, and the recently constructed award-winning House of Music and Museum of Ethnography.
Take a look at this map of the Városliget. It has detailed information about every aspect of the park if you are looking for something specific.
https://ligetbudapest.hu/terkep