When quoting country, state or county names after the name of a town, set commas before and after:

New results were announced at the conference in Osaka, Japan, last week.

British

It is not necessary to say that London is in the UK. For all other UK cities, spell out explicitly that they are in the UK. 

A team of physicists from Manchester in the UK reported that…

US

In text, there will not usually be any need to include state name where referring the following cities: Boston, New York, Chicago, Seattle, San Francisco, Los Angeles and Washington DC (which is not in a state anyway)

For the suburbs of Washington DC (Beltsville, Arlington, etc) quote the name of the town and the state (Beltsville, Maryland; Arlington Virginia) not “near Washington DC”.

Australia

Unless the context makes it clear, always say explicitly that a place is in Australia. And include the name of the state for all cities except Sydney, Melbourne, Canberra and Brisbane.

Canada

Unless the context makes it clear, always say explicitly that a place is in Canada. Include the province for all cities except Toronto, Montreal, Quebec, Ottawa, Vancouver and Edmonton. 

Other countries

Use the anglicized names that appear in the ODE  (Cologne, not Köln; Florence, not Firenze, etc) except for the following: Hannover, Lyon, Marseille.

When name does not appear in the ODE, follow the Times Atlas.