"Let's go to the theatre."
You can, but the meaning changes. 까지 means until, or to a certain extent, so saying "극장까지 갑시다" would mean "let's go up to the theater". I guess it works if you're racing someone, but a more common usage would be something like:
극장까지 좀 태워 주시겠습니까? / Could you give me a ride to the theater?
For years I have suggested DL do something to add context. Erudis is absolutely right; your translation is technically correct, but are you properly interpreting the thought intended? We can't really know without context, though the example given is certainly the most expected.
They could use "cues" in parenthesis. (The play starts in an hour, sir.) Let's go to the theater." That would establish both the level of formality and the purpose for going. as opposed to (I need some fresh air / excersise.) Let's go to the theater. (without the intent of going in, in which case, 까지 would be used.
I used 극장에 가자, which would not be correct with the first clue, but would fit with (Honey, we haven't seen a play in a while) Let's go to the theater.