Nara's a must do day trip if you're in Kyoto or Osaka. It's full of historic buildings and has the free roaming deer that has become popular amongst tourists.
You can easily get to Nara from Kyoto and Osaka stations, ending at Kintentsu-Nara station.
Nara Park is a short walk from there, and you'll notice small cafes and shops selling Japanese items as you get closer to the park. I recommend checking out Kōfuku-ji, Kasugataisha and Tōdai-ji, all of which are historic.
Tōdai-ji is probably the most famous in the area. It's a few hundred yen to enter (depends on which ticket you buy, there's also a museum). One of the interesting activities on the inside is attempting to go through a small square in one of the wooden pillars. Little kids have no problems but I haven't taken the risk - it's tiny!
There are places scattered around the park that sell senbei (Japanese crackers) for the deer. You can bow to the deer and they'll bow back, then feed them. You can get extremely close and personal with them as they are accustomed to interacting with people, but they do get aggressive at times and try to grab that senbei out of your hand.