You'll want to browse the collections at Ural Geology Museum, Yekaterinburg History Museum, and Fine Arts Museum. 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 catch a show at Yekaterinburg Circus, Puppet Theatre, and Amphitheatre.