#!/usr/bin/perl -w

use strict;
use diagnostics;

mysub();


sub mysub{

my $vari = hereistheip();

print "This is the IP you entered --> $vari\n";

local $^I = ".bak";

@ARGV = "stuff";

    while (<>) {
        s/FOO/$vari/i;
        print;
    }
}

sub hereistheip{

print "Enter a valid server IP \n -->  ";

my $myip = <>;
chomp $myip;

return $myip;
}
[download]

You're reading from the console via the <> operator. The script will only continue to the next file (as given via @ARGV) once the current file has been completely read. If you want to continue that dangerous road, you'll have to type an EOF (^Z on Win32, ^D on Unixish operating systems) after you've entered the IP address.

Let me suggest ditching the in-place-edit magic and reimplementing the loop yourself. That way, you can do away with the diamond-operator/@ARGV magic and use explicit filehandles. Maybe it's already enough to change hereistheip to the following:

sub hereistheip {
    print "Enter a valid server IP\n -->";
    my $myip = <STDIN>;
    chomp $myip;
    return $myip;
};
[download]

But I really think you're better off ditching the whole in-place approach and doing it yourself.

Holy crap I feel stupid. I equated <> to be the same at <STDIN>.
Problem solved...