You might want to spend some time browsing the exhibits at Yekaterinburg History Museum, Nature Museum, or Sverdlovsk Railway Museum. Sights like Church of Ascension, Rastorguyev-Kharitonov Palace, and Church on Blood in Honor of All Saints Resplendent in the Russian Land are landmarks to visit in the area. You can watch performances at Amphitheatre, Yekaterinburg Circus, and Puppet Theatre if you're interested in local theater.