Instead of many ifs and explicite nexts, I'd use given/when:

use 5.010;

use strict;
use warnings;

my $low = 1;
my $high = 1000;

my $goal = $low + int rand $high - $low + 1;

sub prompt {print "Enter a number between $low and $high: "}

prompt;
while (my $guess = <>) {  # Allows you terminate the program with ^D
    $guess =~ s/^\s+//;
    $guess =~ s/\s+$//;
    given ($guess) {
        when ("") {;}
        when (/[^0-9]/) {say "Please enter digits only";}
        when ($goal) {say "You won!"; exit;}
        when ($_ < $low || $_ > $high) {say "Please stay within limits
+"}
        when ($_ < $goal) {$low = $_ + 1}
        when ($_ > $goal) {$high = $_ - 1}
    }
}
continue {prompt}

__END__
[download]