I agree with TeacherRome. You are correct in thinking that “nasaan” would be the appropriate word to use there. If we are to make a literal translation of that sentence it should really be “Nasaan ang mga istasyon ng tren?”.
When “saan-saan” is used in place of “nasaan” the literal translation would be “At which locations are the train stations?”.
However, whichever form of the question is used the same answer may be expected.
I suppose that “saan-saan” was used in that example only for the purpose of illustrating that it is the plural form of “nasaan”.
“Nasaan” would require the use of “mga (istasyon)” to indicate plurality, but “saan-saan” need not use “mga” anymore since it is already indicative of plurality. Hence, with “saan-saan” the question may even be stated as:
Saan-saan may istasyon ng tren? = At which locations are there train stations?
The example given by TeacherRome (“Saan-saan matatagpuan/makikita ang mga istasyon ng tren?” = At which locations/Where will I find/see the train stations?) is correct. However, the verb “matatagpuan/makikita” was added to the equation and because of that, “saan-saan” became associated with that verb and is no longer the plural form of “nasaan”, but of “saan” instead – saan matatagpuan/makikita. It is grammatically incorrect to say “nasaan matatagpuan/makikita”.
So, “saan-saan” is the plural form of “nasaan (where is something/somone)” and “saan (where)”.