You might want to spend some time browsing the exhibits at Nature Museum, Yekaterinburg History Museum, or Boris Yeltsin Presidential Center. While you're exploring, swing by Rastorguyev-Kharitonov Palace, Church of Ascension, and Church on Blood in Honor of All Saints Resplendent in the Russian Land to learn a bit about the area. You can watch performances at Yekaterinburg Circus, Amphitheatre, and Puppet Theatre if you're interested in local theater.