No visitor to Kyoto should miss the Imperial Palace, which, although neither grand in the tradition of sprawling medieval castles nor opulent in the tradition of the renaissance European royal palaces, is one of Japan's most historically significant site. It is this nation's most powerful and commanding site. It has captivated the heart of the nation for 2,500 years, and is still today a spiritual center of the old Japan.
The Old Palace is mostly free of frivolous trappings. In its simplicity hid an extremely ordered, hierarchical society. A couple of things in particular illustrate this one dominant principle of Japanese society. For example, there are separate entrances for the king, the queen, high-level shoguns, and lower-level officials. The doors are distinguished, not by the amount of gold or other precious metals (though you do find gold leaf decorations on some of the palace doors), but by the thickness of the cypress roof, with the king's entrance having the thickest roof overhead. Even the empress was not allowed to use the king's entrance unless she was accompanied by the king. Another example is the waiting room for those seeking audience with the king. There are three waiting rooms: the room closest to the king's throne is the lion room (denoted by the painting on the shoji screen), followed by the crane room, and finally the cherry blossom room. The lion room is highest, i.e., you have to step up from the crane room to reach the lion room. The same goes for access to the crane room from the cherry blossom room. Even the colors of the tatami mats graduate from lighter to darker yellow.
The gardens and the Palace themselves form the center of Kyoto, and are thus a vital and necessary focal point for the tourist. Take a walk through the gardens and along the paths between them. I find that walking in the footsteps of countless old rulers is a powerful and humbling experience. As you walk through the gardens and approach the Palace, do be mindful of its tremendous significance, and that it was the seat of the chrysanthemum throne for two and a half millenia.