If you want to see a show while you're in town, try and grab some tickets at Rezo Gabriadze Theatre in Tbilisi City Centre. If you enjoy the show and want to see another, Rustaveli Сinema is just a short walk away.
If museums are on your list of things to see, you might want to browse the collections at Art Museum of Georgia in Tbilisi City Centre. You can also discover the cathedral and churches in the area. If you want to see more of the museums in Tbilisi, you can easily walk to Georgian National Museum or National Gallery of Georgia.