Visiting the old town doesn't take long since the reconstructed area is rather small, and I don't think your kids will enjoy the main sights of the old town, the museums, very much. I think they will like the Armoury, the Turkish Chamber and the Transport Museum (which is not that big).
After WW2 and the destruction of the old town the area around the Blue Wonder bridge became the new center of the city. This area is very nice and should be visited too. Around the 1930s it was the most expensive quarter of Europe. It has vineyards, a wine village, beer gardens, posh villas, castles, a funicular and a suspension railway.
You can get to the Bastei either by steam boat or train, but maybe your kids will get bored after 30min on the steam boat. Take the train to Wehhlen, and there you just have to use a ferry to get to the other side of the river.
With kids I would also recommend to see Königstein fortress (which is also in Saxon Switzerland). You can do both on a single day if you start early.
And I would also recommend to see Meissen. It offers a picturesque old town overlooked by a mighty castle (and a cathedral), something all kids like. Meissen too can be done either by train or steam boat.