The royal park aka Stromovka (strom means tree) is a large English style park with a long history. It was probably founded around 1268 by the king Přemysl Otakar II. When it was opened to the public a few centuries later, it became a popular spot for Prague citizens.
Nowadays Stromovka is one of the most popular parks in Prague. In this case, size really matters – although many people go there, you will not have the feeling that the park is overcrowded. Depending on the season, people are walking dogs and kids, cycling, rollerblading, having picnics, playing frisbee etc. You can also meet horse riders (there is a riding-hall nearby).
For me, a stay in the park is not complete without some refreshments. Try the place called Vozovna where you can get something to eat or drink or one branch of the popular chain Lokál located just few steps from Stromovka.