Kuchajda Lake is a good spot for a quick run just north of the city center, in the Nové Mesto area. A paved 1.5 km path circles the lake, with water views the whole way. It’s a popular spot for locals, with a couple of restaurants and a pub just off the path. The whole area is sort of a sports center, with Pasienky Stadium (nice oval track!), National Tennis Center, and the Ondrej Nepela arena.
For a longer run, Pasienky Stadium just to the southwest has a great oval track for running. And you can head due south for less than a km to add a pretty 1 km loop on a clay path around Štrkovec Lake adjacent to the Fischer Games Casino, in Ružinov. You can then head a little east to the Park Andreja Hlinku, with its popular fountain, and over to Park Ostredky.