I know this is a little late, but if someone else comes across this looking, you can now use public_path(); in Laravel 4, it has been added to the helper.php file in the support folder see here.
You can use base_path() to get the base of your application - and then just add your public folder to that:
$path = base_path().'/public';
return File::put($path , $data)
Note: Be very careful about allowing people to upload files into your root of public_html. If they upload their own index.php file, they will take over your site.
The best way to retrieve your public folder path from your Laravel config is the function:
$myPublicFolder = public_path();
$savePath = $mypublicPath."enter_path_to_save";
$path = $savePath."filename.ext";
return File::put($path , $data);
There is no need to have all the variables, but this is just for a demonstrative purpose.
Hope this helps, GRnGC
Source: Stackoverflow.com