I think that the smallest harness is the Petzl "Quistiti", an under-the-legs and over-the-shoulder harness; most gyms have them. While coaching the Junior team at the Dover Gym, I have seen the 4 and 5 year old siblings of team members climbing in them and they fit quite securely. With a little coaxing at a young age, you will find that they grasp climbing very quickly and will amaze you with their progress!
I agree with Al's recommendations for top roping areas, particularly the North End as I think kids would look at negotiating Child's Play and Kiddy Crack as a more impressive accomplishment than a slab climb. The first pitch of Beelzebub (5.4) is also a good one. Pawtuckaway has some very nice steeper slabs and cracks, but not too steep, the only downside is that for the next couple of months the black flies will leave you quivering in fear. Yet another option is some of the climbs on Echo Crags, or closer to the Valley, Square Ledge in Pinkham Notch. The latter is easy with a terrific view; I think that would be my #1 choice.
Personally, I think that most kids would have a much more enjoyable introduction to climbing in a good gym, where the environment is controlled, there are no bugs, and considerably more options, etc. Once they have been introduced in this way, the transition to outdoors is much easier. If they haven't climbed before, at least get them to a gym once beforehand to learn the basics and get comfortable with the gear.
I've been through all of this with my daughter; you can read about our adventures by visiting http://www.angelfire.com/ne2/edge/travels.html
. It is a reprint of an article that I wrote for the Rock and Ice USCCA supplement three years ago. I wouldn't trade the time I spend climbing with her for the world...