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 Church on Blood in Honor of All Saints Resplendent in the Russian Land, Rastorguyev-Kharitonov Palace, and Church of Ascension to learn a bit about the area. You can watch performances at Yekaterinburg Circus, Amphitheatre, and Ural State Variety Theater if you're interested in local theater.