An amusement park, Praterstern, in Donau Insel island, Vienna. You can spend full day there with your little ones and may be you would find few rides alluring enough to give you an adrenaline rush.

Definitely go to Schönbrunn Palace. The inside might be more suited for adults, but they have beautiful grounds and gardens, plus a zoo for the kids.

http://en.wikipedia.org/wiki/Schönbrunn_Palace

Bill, I’d also recommend the Naturhistorisches Museum (Museum of Natural History) because what kid doesn’t love dinosaur bones? :) Other activities kind of depend on the time of year you go to Vienna, because I can think of many activities kids would enjoy, but they’re mostly outdoor ones (which you mightn’t want to do in February!).

@desperado1306: amusement park Prater is not on Donauinsel island – see http://www.prater.wien.info/index-e.html.

You’ll find info about the children’s programme at Schönbrunn palace at http://www.kaiserkinder.at/index.php?id=54. Depending on the weather, you may want to visit the Schönbrunn zoo – see http://www.zoovienna.at/e/index.html. There is the Zoom children’s museum in “Museumsquartier”, an area with several museums – http://www.kindermuseum.at/.
There are a lot of interesting events for children at the national library (but most probably in German) – http://www.onb.ac.at/services/veranstaltungen.htm.

I agree with everyone – definitely visit the Prater amusement park. Another recommendation I have for you (should it still be relevant!) is the Haus der Musik.
It’s an interactive museum all about music and sounds, which sounds terribly boring but it will keep everyone (kids and adults) entertained for hours. It has a bunch of different activities, and near the end theres a conduct-an-orchestra “wii” type activity, which was for me the best thing I’ve ever seen in a museum. It’s really fantastic, definitely don’t miss it.
Here’s the web address: http://www.hausdermusik.com/en/2.htm
It’s also right in the center of the city.
Depending on what time of year you go, also, I would recommend going to Schwedenplatz (in the city center) and getting ice cream. It’s just one of those things you have to do in Vienna.
You could also go to the info center and check out what’s on at the Volksoper, they might have some kid-friendly ballets or something (lots of bright colours and funny things – definitely not your typical ballet).
Have fun!!! Vienna is a beautiful city with heaps to do.