How to get top two occurrence of each city based on timestamp which gets populated in the table.

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How to get top two occurrence of each city based on timestamp which gets populated in the table.
In my table every time few city names gets poopulated with some data. i want to prepare 1 query which will retrieve only two occurrence of each city and then it will display other city.

example :

cityname column1 column2 last_update_date
delhi E F 20/01/2017 12:05
agra A B 20/01/2017 12:04
agra B C 20/01/2017 12:03
agra c D 20/01/2017 12:02
agra D E 20/01/2017 12:01

o/p should be:

cityname column1 column2 last_update_date
delhi E F 20/01/2017 12:05
agra A B 20/01/2017 12:04
agra B C 20/01/2017 12:03

What I have tried:

i can't think what i can use please suggest