The “standard tour” of Uzbekistan will take you to 3 WHS – Samarkand, Bukhara and Khiva. Unfortunately the direct route (6hrs by bus) from Samarkand to Bukhara misses out the country’s 4th WHS – the historic town of Shakhrisyabz. If you have your own transport you can fit in Shakhrisyabz and still get between Samarkand and Bukhara in a day - around 1.5 hours to Shakhrisyabz, 2 hours to see the town, another 2 to Qarshi and then another 3 to Bukhara. By bus would need 2 days.
So, is Shakhrisyabz “worth the detour”? It was the home town of Timur (Tamerlane) and most of the sites date back to him or his grandson Ulughbek. Timur himself has been resurrected since Uzbek independence as a great Uzbek hero after years “in the doldrums” under Soviet rule and an enormous statue of him dominates the town.
The town has a number of blue domed mosques and mausoleums. Unless you are an expert in Islamic architecture or Central Asian history you will probably not get a great deal more “value” out of Shakhrisyabz’s sites compared with those of the 3 other WHS towns. Shakhrisyabz doesn’t exude the history and “mystery of the east”of Bukhara and Khiva or have the magnificence of Samarkand. It is however much smaller, much less frequented by tourists and in essence much more “Uzbek” than these places. In my opinion if you do have your own transport or are not short of time it is worth the extra effort to take it in.