Exporting incoming email address by date range for all mailboxes

Question

I run a Small Business 2011 Standard server using Exchange 2010 for a small municipality.  A public records request was made for all email address that emailed any employee of that city between 1-1-2013 and 3-6-2014 .  There are about 160,000 emails
for that date range but how can I just export a log of the senders email address with a time stamp?  Thank you in advanced for any help you can give.
I should add that All logging is at defaults values 
I found a "work around",  I have a Barracuda Message Archiver, I did a search of the date range and exported it to CSV, then imported it in to Excel and just deleted the extra data.
Thanks for the fast replies 

Answer 1

Good point, Belinda. If you have that time period within your log retention, then you should be able to do something with the Exchange Shell. This is a bit rough but could serve your purpose:
#--- This finds the email addresses of the users whose city is set to Sydney.
$Sydmbx = Get-ADUser -Filter {City -eq "Sydney"} -Properties homemdb, proxyaddresses | ?{$_.homemdb -ne $null}
$Sydmbx | %{$Sydaddresses += $_.Proxyaddresses}
$Sydaddresses = $Sydaddresses.TrimStart("SMTP:")
$Sydaddresses = $Sydaddresses.TrimStart("smtp:")
#--- Enter your HT servers here
$ExchServ = @("exch01", "exch02")
#--- This creates an object which lists senders who have sent to our recipient addresses, the timestamp and messageid.
$Report =@()
foreach ($server in $ExchServ){
foreach ($addy in $Sydaddresses){
$sentmail = Get-MessageTrackingLog -Server $server -Recipients $addy -Start "01/01/2013 12:00:00 AM" -End "06/03/2014 2:00:00 PM" -EventID Deliver -ResultSize Unlimited
$sentmail | foreach{
$Trackobj = New-Object PSObject
$Trackobj | Add-Member -MemberType NoteProperty -Name "Recipient" -Value $addy
$Trackobj | Add-Member -MemberType NoteProperty -Name "Timestamp" -Value $_.Timestamp
$Trackobj | Add-Member -MemberType NoteProperty -Name "Sender" -Value $_.Sender
$Trackobj | Add-Member -MemberType NoteProperty -Name "MessageID" -Value $_.MessageID
$Report += $Trackobj
$Report
You can change the location to suit yourself as long as you populate "City" in AD and the server names with your own servers.