Eurovea is a rather big building complex containing shops on four floors, flats and offices, the Hotel Sheraton, cinema city as well as plenty of restaurants right on the bank of the Danube, the river of the capital.
The key of success is that most of the bars and restaurants have their entrance as well as their considerably sized terraces outside the building; therefore you do not have to fight through the shopping center itself. While enjoying your drink or meal, you can enjoy the really nice view of the river, the Old Bridge and the new Apollo Bridge, the mall, where crowds of people stroll during warm days in order to find a place where they could do what you are doing :).
Here I would mention that the Eurovea mall has also became a kind of a show window in town. If you want to see and be seen, just come here and promenade. I can highly recommend this aesthetic experience for male travelers who can enjoy the fashion show of beautiful Slovak girls here. (For women I would rather recommend shopping :).)
I can state that you can feel relaxed here, it is neither too posh, nor too snobbish; the river and its shore surely ensure the chill out factor :).