The timezone in one location isn't always the same - for example, the UK is BST (GMT + 1) between March and October. Use one of the timezones supported by PHP:
http://php.net/manual/en/timezones.php
If you do go ahead using numbers, either store them as hours or minutes. Store timezones west of UTC/GMT as negative numbers. For example, the US East Coast would be -5
(hours) or -300
(minutes) - assuming it's 5 hours behind.
Then, add this to the timestamp - the negative or positive will handle the rest.
// for 5 hours behind when stored as hours (-5)
$now = time() + ($offset * 60 * 60);
// for 5 hours behind when stored as minutes (-300)
$now = time() + ($offset * 60);