Thanks everyone for all of the suggestions. I'm going to start my research, but the Vienna Woods with Liechtenstein castle sounds like it could be good choice, as my kids love to visit castles and it would be nice to get out of the city for a bit. I'm glad to hear the feedback on the boat to Bratislava as well; I had seen that online and was thinking it might be fun (but apparently not). I"m also tempted by bergruine, though I'll have to figure out how much time is involved in getting there.
I also appreciate the suggestions in the city itself- I've definitely been planning to visit both palaces. I'd love any additional suggestions for favorite restaurants to visit while we're there.