The following are all fine too:
I went to see a movie last night.
I went to the cinema last night. (Note that in BrE, this doesn't just mean "I visited the building called a cinema. It means that you went to see a film.)
I went bowling last week.
I went to watch a TV show being filmed on Tuesday.
I went shopping in the shopping mall on Friday.
I went swimming in the sea on Saturday.
I went swimming at the local swimming pool on Saturday.
Was there a particular reason that you thought "go/went" could only be used with outdoor activities?
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