Put a circle of radius 10 at the location of the world's largest city. Now put one for the next largest city that doesn't touch the circle you already placed. Keep going, making sure no previously placed circle is touched!
Data for 1M cities from citypopulation.de, data for smaller cities from geonames.org
Answers are sorted alphabetically
Cities with no more than 10,000 inhabitants are only considered if they have no larger city within 100 km