You might want to spend some time browsing the exhibits at Yekaterinburg History Museum, Ural Geology Museum, or Boris Yeltsin Presidential Center. While you're exploring, swing by Rastorguyev-Kharitonov Palace, Church on Blood in Honor of All Saints Resplendent in the Russian Land, and Opera and Ballet House to learn a bit about the area. You can catch a show at Puppet Theatre, Yekaterinburg Circus, and Amphitheatre.