"We go to the theater today."
Translation:Andiamo al teatro oggi.
Both are OK, but the emphasis is different.
Vado al teatro - I go to a specific theater that is known by the context (maybe I drive there in order to pick up someone).
Vado a teatro - I go to [a/the] theater, in purpose to watch a play (or doing another thing in there). The "being" in the theater is what emphasized, not the specific place.
Both could be said in the situation of going to see a play, "al" just don't say implicitly that you will watch a specific play, and "a" do not refer to THE specific theater, but context can resolve that.
@GidiZisk Following your reasoning, I would ask you to use the word "cinema, as you know, in Italian it's the same word"... how would you say in Italian "I go to the cinema today".
We say "vado a teatro" if we go to the theater, it doesn't matter what you're going to do there, but usually it means going to watch something. But if you're going to a specific theater, you use "al"... "vado al teatro Sistina" (I go to Sistina theater).