Select the newest records of different columns

Question

Sample data:

Date       City       Name
--------------------------
1/2/2011   New York   John
5/1/2011   Chicago    Matt
2/1/2011   Chicago    Mark
9/2/2011   New York   Johnny
3/1/2011   Boston     Phil
5/1/2011   Chicago    Martin
9/1/2011   Boston     Neil
2/2/2011   New York   Nicholas
1/2/2011   New York   Tom
3/2/2011   Chicago    Eric
5/1/2011   New York   Jack
12/1/2011  Chicago    Peter
11/2/2011  New York   Paul
9/2/2011   Boston     Steve

I need to take 3 more recent reports about every other city. I mean the three newest recordings of New York, Boston and Chicago.

I know that I can do this in PHP, but imagine that there are thousands of records in this table, it is not useful to take all the records and transfer them to PHP: P

How is this possible in a single MySQL query?

Thank!