First, I have to say some of the dates these cities founded are confirmed by their local government and history experts though they might be amazing.
Welcome to correct and discuss my list
1.for non-coastal cities in the continent
Hard to choose 10, so I get more
Beijing (Peking) founded in 1045 BC
(just a acient city in its modern area, being capital of one states in 600sBC, being capital of Jin Dinasty in 1153, rebulit by Mongols in 1258, rebulit and renamed Beijing in 1403)
Xi'an (Chang'an) founded in 1000s BC
(rebulit many times, flourish in 600ADs being capital of China for 1191 years)
Luoyang 770BC
Kaifeng 700sBC (flourish in 1000ADs, before invade of Mongols)
Suzhou 541BC
Yangzhou 486BC (flourish in 1000ADs, before invade of Mongols)
Nanjing 472BC
Chengdu 311BC (a city never completely destroyed, have a mass earthquake recently)
Shenyang BC301~296
LanzhouBC 241
Chongqing(BC 1100s but named Chongqing in 1189)
Wuhan(BC 1500s but disappear in BC 1100s, 3 cities together renamed Wuhan in 1927)
Lasa(Lhasa) 633 AD
(Not ours that time, but Tibet belong to China since the domination of Mogols 700years ago)
Wulumuqi(Urumqi) 1755 AD (So we call there "new horizon")
II- Coastal Cities on the Home Continent
we don't forcus on navagation and navy...and many ancient coastal cities fall...
Hangzhou(Lin'an) 221BC
Guangzhou(Canton) 214BC
Ningbo 821AD
Xianmen(Amoy) 1387AD
Tianjin(Tientsin) 1404AD
Shanghai 1553AD
Sorry to forget it...
Qingdao(Tsintao) 1891AD (Former German Colony)
Macau (Aomen 澳门

Maybe 1557AD (Who knows what Portuguese did there?)
Hangkong 1841AD (actually Xianggang香港... means fragrant harbor Former English Colony)
Dalian 1899AD (Former Russian Colony)
Shenzhen 1980AD (the fastest growing cities, use 20 years from a small villige to a city with 11 million population)
3- for non-coastal cities in another continent
I'm sorry that we don't have, but maybe there's many Chinese in some cities nowadays...
4- for coastal cities in another continent
I think islands near continent should count, isn't it? So...
Haikou several hundreds years ago... can't find.
Sanya
Taipei(Maybe Taibei is better) 1875AD (Taiwan was invaded by Niederlander, Spainish and Japanese, but it's part of China undoubtly, no matter it's PRC or ROC)
Kaohsiung(Gaoxiong)