You might want to spend some time browsing the exhibits at Ural Geology Museum, Yekaterinburg History 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 Novo-Tikhvinskiy Convent to learn a bit about the area. You can watch performances at Yekaterinburg Circus, Puppet Theatre, and Amphitheatre if you're interested in local theater.