The Kaiserwasser is connected to the Alte Donau river, but is almost wholly enclosed. On its Southern edge there is a partly shaded, large grassy area which is a popular picnicking and swimming spot in summer. There are a few concrete steps to get into the water, which is acceptably clean (I swam three days and had no ill effects!); the bottom is a little stony but you don't need any footwear.
As it's not part of the main river, there are no boats, and the water warms up quite quickly in sunny weather. It shelves gently down from the shore; I could start swimming about 5m out, and was out of my depth when about 20m out, so is relatively safe for children, too. And as a small body of water there's no tides or waves. The biggest danger is probably from swans, which sometimes swim in the area, but they seem used to human swimmers and ignore you unless you get too close.
There are no lifeguards, showers or lockers, so be careful not to leave valuables unattended. Having said that, it also seems to be an area with very little crime, so I risked leaving my hotel room card (which had no room number on it) and a basic ID in case of emergency with my clothes. It's about 5 minutes’ walk from the Vienna International Centre (and U-bahn); if you are very well organised you can get across to it for a quick swim in a lunch break from a meeting!