The City of the Dead tour is a kind of mix of ghost walk horror story and history lesson. You'll visit various locations including an underground medeival street, the Dead centre of the city where a usurper to the throne was tortured for 3 days (very imaginatively), a grave yard (1 in 50 of the graves when moved had fingernail marks on the inside), and lots more. The bits I've told you won't detract by the way they're just teasers.
The tour folk I went with were Mercat tours, I think it was about £20 for a family ticket 2adults, 2children.
Hope that helps, oh and at the bottom of the Mile there's Dynamic Earth which my kids said was really good (I sent them there to get rid of them for an hour or so ).
There is lots to do, your wife will want to go to Harvey Nick's and Jenners, so when the kids are out and your wife's shopping you're free to roam the loads of kilt shops on the Mile.
Cheers Rhino