If you want to see a show while you're in town, try and grab some tickets at Lermontov Russian Drama Theatre in Almaly District. If you enjoy the show and want to see another, Almaty Opera House is just a short walk away.
If museums are on your list, you might want to check out the upcoming exhibitions at Geology Museum in Medeu District. If you want to see more of the museums in Almaty, National Museum of Kazakhstan and Kazakhstan Museum of Arts aren't far.