He said that she had come there the day before.
Coming is motion toward a place, whereas going is motion away from it, whether the place is "here", "there", or even "yonder". The verb should be preserved. For example: "I came to Hong Kong yesterday". It is said that I came to Hong Kong yesterday. It was said that I had come to Hong Kong the day before. It was said that I had come there the day before.
No. If the person reporting the 'coming' is in New York, then s/he has the choice of seeing her/himself in Hong Kong ("X said that I had come to Hong Kong") or in New York ("X said that I had gone to Hong Kong").
The other possibility, of course, is He said that she had come here the day before. Whether "here" or "there" depends on where "he" is.
If, as you say, we have a choice between 'here' and 'there', then we have a similar choice between 'come' (here) and 'go' (there).
There are no hard and fast rules with reported speech; so much depends on the speaker's/writer's perception of events. The 'rules' given in course books are useful guides to what people frequently say/write, no more. The same words can be reported in different ways; for example:
Situation:
Jutta lives in Stuttgart. Jon lives in London.
18 March, 2009: Jon flies to Stuttgart to see Jutta.
19 March, 2009, Jutta says to Donald, "Jon came to Stuttgart to see me yesterday".
Donald later reports this:
19 March, 2009, Donald (in Stuttgart):
Jutta told me that Jon came to Stuttgart to see her yesterday
23 March, 2009, Donald (in Stuttgart):
Last Friday, Jutta told me that Jon came/had come to Stuttgart to see her the day before.
24 March, 2009, Donald (in Moscow):
Last Friday, Jutta told me that John came/had come to Stuttgart to see her the day before. [Donald is reporting Jutta's words closely, seeing himself in Stuttgart with Jutta as she spoke the words.]
24 March, 2009, Donald (in Moscow):
Last Friday, Jutta told me that John went/had gone to Stuttgart to see her the day before.[Donald is distancing himself from the conversation with Jutta. He is reporting, from Moscow, the words of Jutta in Stuttgart.