Why sometimes we use only 'à' and sometimes we use 'au' :

Hi Diagenes, 

Because most towns and cities don't have an article (le, la , les) in front of them, you will just use : 'à '

Je vais à Paris, à Rome, à Madrid, à Londres, à Calcutta, etc...

N.B. With some towns, cities and villages which have an article in front of them as Le Havre , Le Caire (Cairo) it will follow the rule - 

Je vais au Havre, au Caire, etc...

Countries have an article in front of them so it will depend whether they are feminine ( La France) or masculine ( Le Brésil) , or plural (Les États-Unis).

e.g. Je vais en France, au Brésil, aux États-Unis...

Take a look at the following lesson which will give you more examples - 

https://french.kwiziq.com/revision/grammar/use-en-with-feminine-countries-and-aux-with-masculine-countries-to-say-in-or-to-prepositions

Hope this helps!

Hi Martin, 

Dont' believe everything you read on Google translate -

London is Londres!

So :

Je vais à Londres is correct .