Find a shady space, talk with some of the locals and enjoy the atmosphere of Ala-Too Square. It's a nice spot to take a break from sightseeing.
You'll be spoiled for sightseeing choice when in Bishkek. Ala-Too Square is an ideal place to kick off here, but there are many other worthy spots to appreciate. Bishkek Park Shopping Center, Parliament of the Kyrgyz Republic, and Osh Bazaar are not far from the modern public area and will fill in your day nicely.