This garden it's really close to the Kálvin square. If you are tired because of the walking and you feel you should make a rest, it's a good choice to visit here. Here you can lie down to the grass. There are lots of banks to sit as well with many shades of the trees. It's a cozy place for children with a playground. Here is available an public toilet for free. At the corner there is a really cute coffee shop to chill a little. In the neigborhood, there is the renting bike station.
Orczy garden is a quite big green area. Here is a lake with a nice buffet. In this garden there is a possibility to lie down to the grass. If you need to use the bathroom, you are looking for the small house, there is the public toilet for free. From here you can also rent a bike if you want.
At the Kopaszi gát you can find an entertainment place, it's called Dürer Garden. This area has a really good vibe and you feel free to lay down to the grass. You can find more restaurants here and you should make a try with the ice-cream too. There are more public toilets for free in the separated tiny houses.
I'm sure that you have already heard about this park. This is the most visited park because there is the ZOO and the Széchenyi Thermal bath too and it's nearby the Hősök tere. You shouldn't skip the roses garden especially from Spring till Autumn. City park looks beautiful and cozy however sometimes is really busy because of the public events.