There doesn't seem to be any read-out of Lat/Long in Google Maps, but other folk have developed that facility.
The best one is at:
http://www.earthtools.org/
Same as standard Google Maps but with big cross in centre.
Double-click to zoom into area you want, re-centre as you go, read out Lat/Long on panel at left.
Brilliant!
This may not be the solution if you 'don't know where the place is', but worth bookmarking anyway.