Largest City (urban area) - New York (8,683 sq. km.)
Largest Capital City (urban area) - Tokyo (6993 sq.km.)
Largest City (population) -
City Proper - Mumbai (14 mn)
Urban Agglomeration - Tokyo (35.7 mn)
Largest Capital City (City Proper population) - Moscow/ Seoul (Both have approx. 10.5 mn people)
Most Densely Populated City/ Capital City - Dhaka (45,508 people/ sq.km.)
Richest City (GDP) - Tokyo (US$ 1191 bn)
Richest City (Per Capita Income) - Copenhagen
Richest City (Purchasing Power Parity) - Zurich
Smallest Capital City (population) -
1. Adamstown, Pitcairns Island (48) (British Dependency)
2. Ngerulmud, Palau (391) (Newest Sovereign Country)
Note - 391 people live in the whole state of Melekeok in which Ngerulmud is just one village.
Interestingly the Capitol building of Palau located in Ngerulmud is modelled somewhat after the US Capitol.
Oldest continuosly inhabited City - Damascus (Syria)
Some cities where most of the population of the country resides (city states like Singapore, Monaco, etc. are not considered) -
Ulan Bator (Mongolia) - 1,068,000 people of the total population of 2,671,000
Alofi (Niue) - 581 people of the total population of 1400
Stanley (Falkland Islands) - 2,115 people of the total population of 3,150
Koror (Palau) - 14000 of the total of 20000 Palauans reside in Koror
Paramaribo (Suriname) - About 243,000 people out of a total of 472,000
And of course we have Adamstown where the whole population of Pitcairns Island lives.
Note: The population figures may vary depending on the source one refers to.