Samarkand is the site of the iconic Registan - the "sandy place" surrounded on three sides by Timurid madrasahs. You can sit on a bench on the fourth, open, side and take it all in - the turquoise tiles, the slender minarets, the imposing facades. The place attracts a lot of Uzbek tourists too. The madressahs can best be admired from the outside, as their interiors are completely taken over by the souvenir business. Only the middle (Tilya Kori) is worth a visit for its completely gilded interior including golden mosaics.
Somehow it had escaped my attention before that Samarkand has several other grand monuments than this Registan. Probably the best sight of my whole Uzbek/Turkmen tour was Shah-i-Zinda. This is a mausoleum complex, where the tombs are housed in the most ornamental little buildings. They feature all the mosaics and glazed tiles Samarkand is famous for, but on a more touchable scale than at the Registan. The place is also full of Uzbek pilgrims and daytrippers, creating a lively atmosphere (imagine visiting this wonderful site on your way from grocery shopping - I saw many Uzbeks carrying their round loaves of bread with them).
The tomb of Timur (Gur Emir Mausoleum) is the third site worth mentioning. On the inside, it has the feel of a European cathedral, with the tombs in the middle under a cupola and older Uzbeks praying around it.