There are 2 different mitzvot, one of tzedakah (giving charity to the poor) which is accomplished by giving away a few dollars (YD 249:2) and one of maaser (carefully separating 10% or more of your income, see here for more details).
Your question is which non-Jewish organizations count against one's maaser obligation.
In The tzedakah treasury p. 406, R Avrohom Chaim Feuer writes
We provide financial support to the gentile poor (Gittin 61a, YD
151:12) [...] [R Pesach Feinhandler in] Responsa Avenei Yashpei (YD 1:193) maintains that
one may deduct charitable donations to non-Jews from his maaser
obligation. However he does suggest that the concept of darkei
shalom, i.e., fostering harmonious, peaceful coexistence only applies
when the non-Jew asks for Jewish aid. If the non-Jew does not request
Jewish aid and does not expect it, there is no obligation to volunteer
a contribution because there are sufficient non-Jews who can support
In Priorities in Tzedaka p. 82, R Moshe Goldberger writes
One may give to secular or non-Jewish charities in order to promote
peace darchei shalom. It would depend if the money goes for causes
that are in accordance with the Torah. For example, if a [secular
Jewish] community center is open on Shabbos, it is forbidden to
support it with any type of funds.
See also this related answer: What constitutes tzedakah?.