Nur-Sultan (formerly Astana) — second largest city, and capital since 1997. Worth visiting but you only need a few days to get to the most worthwhile sights. *Almaty — largest city, and capital until 1998.
Definitely a must-see. Beside the Soviet-style city, you may want to go to the *Medeu and other places in the nearby mountains. *Turkestan (map) — another ancient city, long a border town between the Persian culture to the south and the Turkic nomadic culture to the north, now majority Uzbek and home to several important cultural-historical monuments.
Train is the most popular way of covering the huge distances between Kazakhstan’s main cities. Kazakh Railways tickets can be bought online.