Imahan (今半) is famous for Sukiyaki but their Shabu-shabu is also delicious. They cost more than ¥10,000. Is it too expensive?
You should definitely try "Onyasai".
At Onyasai, you can have all-you-can-eat shabu-shabu around ¥3,000 ~ ¥6,000. The price differs by the quality of meat... pork+chicken course is cheaper and wagyu beef course is more expensive.
I have been to Onyasai several times and their quality of meat is not too bad. You get to choose two kinds of flavors for soup from more than 10 flavors, and all-you-can-eat course includes other small dishes, vegetables and noodles as well.
It's a chain restaurant and they welcome children, too. By the way, Onyasai belongs to the same group as the famous Yakiniku chain Gyukaku.