Kyoto is the capital of the West in contrast to Tokyo, but Kyoto is rarely called "西京" (Saikyo) and was called so only for a short period immediately after the capital was moved to Tokyo.
東京に対する西の京は京都であるが、京都のことを「西京」と呼ぶことは稀である（東京奠都直後に短期間だけ呼ばれた）。