My kids (now 7 and 11) love backpacking - in particular because they love the whole camping experience. If an overnight is (or becomes) an option then the hike to Chicken Spring Lake, 4.5miles from Horseshoe Meadows, is a nice microcosm of the Sierra - a meadow, forest, streams, a climb up to a pass, a beautiful lake and lots of ground squirrels!
Alternatively, Gilbert and Flower Lakes on the way up to Kearsarge pass are beautiful and sub 5miles round trip.
If you're thinking longer term, I've done the following with mine:
2014 (son, 7yrs old) - Whitney from Horseshoe Meadows over 8 days, 5mi/day.
2015 (son 8, daughter 5) - Tuolumne from Agnew Meadows over 8 days, 4mi/day (I highly recommend this one, I think it's the best 30 mile family hike imaginable - lakes, streams, constant distractions).
2016 (son 9, daughter 6) - Whitney from Onion Valley over 9 days, 6mi/day.
All these paces allowed a lot of time for playing en route and at camp each night, as well as a relaxed hiking pace. I find the kids average 1mph allowing for breaks. Their limiting factor is boredom (i.e. with mental distraction - mind games, stories, chatting etc. they will go all day) rather than any physical limitations.
