I've hiked the loop at MRT, doing it again this spring.
I've also hiked a two day "loop" near the Devil's soupbowl.
Some areas are less desirable.
If you are looking for a week, why not try out Pictured Rocks? you can park in Munising and get transportation to the other end of the trail, water is available at most sites, great views and other options off trail.
How old is your kid?
Isle Royale is awesome for a week long hike.