Now to catch up on some posts I've been meaning to do for a while.
One of the best day trips to make with kids from Kyoto is to the Osaka Aquarium. It is a full day but a lot of fun. I recommend getting the day pass from the Keihan or Hankyu lines. These are available at the information counters in the respective stations. Keihan: Demachiyanagi, Sanjo, Gion Shijo. Hankyu: Kawaramachi and Katsura. They are 2800Y for adults 1400Y for elementary school and include transportation on one of these lines, all subways in Osaka and entrance to the Kaiyukan- you don't even need to wait in line to buy the tickets. Just going to there and back saves you about 500Y but the deal gets better the more you do in Osaka. The tickets get you discounts at other attractions as well.
We went on a weekend. I don't recommend doing that if you can help it. Even though we had the passes, we had to wait in line for about an hour just to get in. Once in it was really crowded for the first few floors. On crowded days I would suggest going down to the bottom and going back to the top later.
When we went we also had dinner at the Turkish restaurant in the Tempozan mall right next door. It is another all-you-can-eat place. Great food and Turkish ice cream for dessert. They even had belly-dancer. J really liked that.
Adults:1680Y, ages 6 and up 890Y. Kids under 5 eat free. Kosher and Halal.