I'm answering based on common, informal speech. Not necessarily proper, well structured English.
"I think I'm gonna go to the movies tonight.
"I think I'm gonna go to the movies."
In the second example, it's okay to drop "tonight" because it's just common and expected that you'll be seeing a movie in the evening.
"I think I'm gonna go see a movie."
"I might go to the movies."
It's my experience (Canada) that this type of speech is more common. You rarely ever hear people say theater or cinema in this context. Typically people will use "movie" or "movies" when describing the act of going to the theater to see a movie, because they're describing the event rather than the location or venue.
Where you will hear people use theater/cinema is in speech directly associated with the location rather than the event.
On the phone, Jane asks Jim where he is. He replies:
"I'm at the theater."
.. rather than:
"I'm at the movies".
... although it would be perfectly acceptable in informal speech and convey the same meaning to use the latter. Again, to illustrate the point about location versus event:
Jane: "Where did you get those cool 3D glasses?"
Jim: "At the theater."
Jane: "Can you grab me a pack of smokes on your way to the theater?"
Jane is a terrible chain smoker and soon she will suffer a premature hypothetical death and no longer be used in my examples.