I may repeat some stuff that's been said, but we went there last summer and it was pretty awesome.
Must do :
We camped at Dead Horse Campground and I didn't even realize that classic U-shaped-river sunset pic was taken there before we booked. You have to go there - get there about an hour before sunset for a good spot (both parking spot and viewing spot).
Canyonlands : The short hike to Mesa Arch is well worth the time. It's about a mile round-trip, and it was the screen-saver on my work laptop for about a year after I took it. You can google it, it's sort of a big deal.
Arches : There are 3 views of Delicate Arch. There is the long one (which I regretfully didn't do, more on that later). The short one (for grandparents with walking canes). And there is another that's about half a mile, does have some vertical, but that is also worth the extra effort. This trail is right next to the short hike and I'm glad I did it - it's not a lot closer distance-wise but i thought the view was better and your kids can climb around a little.
Lessons :
Arches : I've been there twice, and did Landscape arch as the first hike - which was awesome - but it does take a while, and the kids got worn out on the 1st hike and didn't do much else, so no Delicate arch super-hike.
If I had it to do over, I'd hike to Delicate arch. I figure the hike is similar to Enchanted Rock, so very doable for an ex-Texan (assuming you've been there).
If you do Landscape Arch, it's in an area called the Devils Playground (I think) and there are 2-3 really cool arches if you take a right , on the way to Landscape. One is called pine-something I think. You can go there and stand right under the arch. It's not well traveled, despite how accessible it is, and I really thought it was cool.
So - the reason the kids were beat down, is we did a mountain bike ride the day before, and we learned that we are NOT a mountain biking family. We went to some area that was about 1-2 miles past Arches, and they have a paved trail that you can take from the mountain bike area back into town. It's about 7 miles, and it's mostly downhill, until the last mile where we had construction and city traffic, and it really sucked. No idea if they still have construction. Also my daughter got freaked by the speed of biking down 6 miles of downhill, but my son loved it. If you ARE a biking family, it was cool, but I don't think we will be doing it again.
Also - parking gets crazy. We drove right to Devils Playground for an early hike (it was in the summer) and tried to see stuff at the front of the park just after lunch, and couldn't find spots to park. I have read that it clears out by late afternoon, but we were back at the campsite by then.