I don't recall seeing a "new" Mongol city-list, so here's the one I use. Some of these might be a bit iffy - particularly some of the former Soviet Central Asian cities, but I'm fairly sure they were all Mongol at some point (even if only while Gengis Khan turned them into a pyramid of skulls...)
Karakorum
Samarkand
Khanbalik
Tashkent
Bukhara
Ulaanbaatar
Qaragandy
Herat
Bishkek
Bishbalik
Balkh
Balasaghun
Almaty
Dushanbe
Qyzylorda
Otrar
Darhan
Erdenet
Ulyasutay
Hovd
Suhbaatar
Ulaanjirem
Dalandzadgad
Ulaangom
Ulaan-Uul
Borhoyn Tal
Bayanhongor
Tamsagbulag
Tsetserleg
Altanbulag
Choybalsan
Saynshand
Mandalgovi
Ondorhaan
Dzuumod
Nalayh
Dund-Urt
Buyant-Uhaa
Bornuur
Ihsuuj
Jargalant
Ar-Asgat
Dzuunbayan
Dzuunhovoo
Harhiraa
Hohtolgoy
Ogoomor
Habchil Ortoo
Nalihin Dugang
Tsoohor
Tsagaannuur
Tsagaantungi
Uujim
Biliuu
Oygor
Baruunsuu
Delgerhet
Jargalthaan
Nilga Suma
Bayan-Ovoo
Har-Ayrag
Dzogsool
Bayanbaraat