Every city has to have a place where you can escape from the tons of concrete and glass to a tiny piece of nature. You may not have spotted it, as it is hidden behind tall walls, but in Bratislava, it is the Grassalkovich Garden right behind the Presidential palace. It is a well-maintained French-style park where people go to get some rest from cty life, without the need of going miles to get it. There are people walking, coming with children to the playground, or just sitting and chatting on benches or the lawn. Why not take a sandwich and spend a nice picnic lunch break here? The park has a soft surface, therefore people also enjoy it for jogging, although the circuit around it is rather small (some 700m).
As a curiosity, on your discovery of the place, you may notice some stone tables memorializing presidents from all around the world who kindly donated trees to this park. Maybe you can find one from your country of origin ;).