Oh, come on! You probably thought of 2 or 3 examples and thought that covered the entire world. Well, it obviously doesn’t.
Here’s a list of those that do end in N:
Yemen
Yerevan, Armenia
Yangon, Burma
Yunnan, China
Yucatan, Mexico
Yukon, Canada
Yilan, Taiwan
Yunlin, Taiwan
Yasothon, Thailand
And here’s a list where they don’t:
Yardimli, Azerbaijan
Yevlax, Azerbaijan
Yambol, Bulgaria
Yomou, Guinea
Yoro, Honduras
Yazd, Iran
Yamagata, Japan
Yamaguchi, Japan
Yamanashi, Japan
Yanggang, N Korea
Ysyk-Kol, Kyrgyzstan
Yap, Micronesia
Yobe, Nigeria
Yaroslavl’, Russia
Yala, Thailand
Yalova, Turkey
Yozgat, Turkey
Yumbe, Uganda
Yaracuy, Venezuela
Yen Bai, Vietnam
Note that both lists contain things usually labeled prefectures, districts, regions, oblasts, and a few other synonyms of state/province. I didn’t discriminate on that basis – any 1st level administative division was included. Names were taken from this page of the CIA World Factbook.