I have three columns. Column A contains various place names, but only
if they are within a certain city; when the place is outside that city,
the cell in column A is blank. Column B contains the quarter that a
particular event occured. Column C contains a score for that quarter. I
want to find the average score for 2nd quarter 2006 only in that city.

A B C
1 Shinjuku 06-Q2 22
2 05-Q1 54
3 Minato 03-Q1 3
4 Chuo 06-Q2 44

So, it would give me (C1+C4)/2.

I imagined it to be like this, but it doesn't work of course:

AVERAGEIF(AND(A1:A4="?*"),(B1:B4+"06-Q2"), C:C)

Your help is greatly appreciated!