Shakhrisabz is the birthplace of Tamerlane, or Amir Timur, and is probably one of the most unassuming of the tourist attractions. Whereas Samarkand's Registan and Bukhara's Old City are inhabited by tourists and merchants, Shakhrisabz is a small town where locals still mingle amongst the historic landmarks.
Most of these landmarks are in ruins, such as the palace, so don't expect another Khiva, but you can feel more authenticly historical in a place like Shakhrisabz.
Be aware that although this was Tamerlane's hometown, the Crypt of Timur doesn't contain his remains.
You can get to Shakhrisabz from Samarkand by buses or taxis in about two hours. The mountain pass road reveals scenery that is a pleasant break from the gray desolation of most of Uzbekistan, although Shakhrisabz may be a tiresome day trip