You might want to spend some time browsing the exhibits at Wonder Park Galileo, Boris Yeltsin Presidential Center, or Fine Arts Museum. 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, Children's Variety Theatre, and Teatron Maly Drama Theatre if you're interested in local theater.