If you know that the value occurs only once in the array, the [array]::IndexOf() method is a pretty good way to go:

$array = 'A','B','C'
$item = 'B'
$ndx = [array]::IndexOf($array, $item)

Besides being terse and to the point, if the array is very large the performance of this approach is quite a bit better than using a PowerShell cmdlet like Where-Object. Still, it will only find the first occurrence of the specified item. But you can use the other overload of IndexOf to find the next occurrence:

$ndx = [array]::IndexOf($array, $item, $ndx+1)

$ndx will be -1 if the item isn't found.

As mentioned in the comments, if you've developing this in ISE (or another IDE) and previously assigned $eventList with a type cast, like so:

[string[]]$eventList = @()

or similar, commenting out previous lines won't help you - the variable already exists and will have that type bound to it for the remainder of its lifetime.

You can remove any previous assignments with Remove-Variable eventList

Once you've got that sorted, we can move on to actually locating the index. If you're interested in the index of an exact match, use IndexOf():

PS> $eventList.IndexOf('hi')
2

If that isn't flexible enough, use the a generic List<T>, which implements FindIndex().

FindIndex() takes a predicate - a function that returns $true or $false based on input (the items in the list):

$eventList = New-Object System.Collections.Generic.List[string]
$eventList.Add("Hello")
$eventList.Add("test")
$eventList.Add("hi")
$predicate = {
  param([string]$s) 

  return $s -like 'h*'
}

And then call FindIndex() with the $predicate function as the only argument:

PS> $eventList.FindIndex($predicate)
0

(it matches Hello at index 0 because it starts with an h)

You are casting the ArrayList to an array, just remove the cast:

$eventList = New-Object System.Collections.ArrayList

Also, you might want to consider using a List<string> instead of an ArrayList:

$eventList = New-Object System.Collections.Generic.List[string] 

try Something like this:

Copy$array1=import-csv "C:\temp\log.csv"
$array2=import-csv "C:\temp\log2.csv"

#modify founded and output not founded
$toadd=$array2 | %{
$current=$_
$founded=$array1 | where pc -eq $current.pc | %{$_.date=$current.date;$_}

    if ($founded -eq $null)
    {
      $current.city='UNKNOW' 
      $current 
    }
}

#output of $array1 modified and elements to add
$array1, $toadd