The railway trails are brilliant, all of them, although beware the climb at the start of the high peak trail in Cromford – with little kids, better to start at Middleton Top.
I’ve only cycled the Cromford Canal, and I would say that whilst it is nice in winter, even on a summer weekday it is a right pain to cycle on for the number of walkers on the narrow path – if you plan any canal cycling, make sure you all have bells.
I thought Ashbourne, Tissington, that way too, is very nice round there and less busy, or Bakewell / Baslow area where you have hills and rivers, Monsal Trail, Chatsworth farm / adventure playground etc.
If you happen to be in Matlock at any point, go to Matlock Meadows Ice Cream Parlour – short drive up the hill behind sainsbury’s (or bike, but it is a blooming steep road hill for kids), bit out of the way, but great ice cream plus farm animals to see (they also do bacon sandwiches, toasties, coffee etc.). Brilliant place and quieter than it should be.