I think Bali is a great idea and especially for a family with teenagers--they are old enough to appreciate the cool cultural stuff and to participate actively in the outdoor stuff. And it has so much more interesting things to do than hang out at the pool. The only thing that worries me is the time factor, if you are coming from Chicago and dealing with that distance of travel with the required connections. If you can arrange a couple of extra days for the kids to be out of school and tack them on to this vacation period, it will give you a bit of breathing room.
The great thing about Bali is that it's got a bit of everything: culture, architecture, outdoor activities, some nature, beach (though note that Bali's beaches aren't the best on offer in SE Asia). Splitting time in two places is a good idea and Ubud should be one of those places. Ubud town itself is good for a bit of time--the kids will like the Monkey Forest. And be sure to go to at least one evening performance of a traditional Balinese dance. I'm partial to the male 'kecak' dance and chant myself... Ubud is also the staging area for white water rafting (nothing too dangerous, just fun), elephant rides, hikes, and is the handicraft center. For a second area, Seminyak is probably as good as anything.
For a family, definitely consider a villa rather than hotel rooms and particularly in Seminyak.
You probably want to engage a van for at least one day and have them take you around the eastern part of the island to Pura Besakih temple, to see the Agung volcano, Tenganan village, etc. It would be easy to spend a week in Bali and be doing something different every day, and still leave something for a future visit.
One thing: Nyepi (Bali's day of silence) is March 23, 2012. The airport will be closed on this day, and other aspects of life affected as well, including for tourists. So check your Spring Break calendar and if Nyepi falls during your vacation period in Bali, read up and be prepared to deal with it.