Nara is a must do day trip if you're staying in Kyoto or Osaka. It's full of historic buildings and has the free roaming deer that has become popular amongst tourists. The deer has even become the city's official mascot, named Sento-kun.
You can easily get to Nara from Kyoto and Osaka stations, ending at Kintentsu-Nara station. I've never actually stayed over, but I've found that a trip out to Nara does require a full day.
Nara Park is a short walk from the station, and there will be small cafes and shops selling Japanese items as you get closer to the park. I recommend making sure you check 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 rice crackers) for the deer. You can bow to the deer and after they bow back, feed them. You can get extremely close and personal with them as they are accustomed to interacting with people, but some of them can get aggressive at times and try to grab that senbei out of your hand. I'm sure they come across people who tease them with it.