Where to a place a custom php file in the directory I have a hard coded form that i need to send to a php page that i have built. With drupal i am a bit confused on where i would place this php page so it doesnt cause any problems.

I was thinking here but i wanted to check first.
/httpdocs/newsite/PHP-HERE
(Same directory as index.php)

Where would i place this php page?
Everything including forms can be integrated nicely within drupal. i would recommend reviewing FAPI. it will save you time/effort in the end. 

however, if you absolutely need this not to be built around/within/whatever using drupal's FAPI, what i would do is put the page either directly in your theme folder or make a subfolder and drop it in there. so lets make many assumptions here (awful i know). say your form is called newform.php. rename it to page-newform.tpl.php and drop it into one of those folders. create a page just to give you a node place holder and a path like /newform. then in your template.php file under the THEMENAME_preprocess_page() function, check the URL with either $_GET['q'] or arg() (arg is preferred). if the url is going to /newform simply adjust your $variables['template_file'] to be something like $variables['template_file'] = 'page-newform'. this will pick up your page specifically.

so with a lot of assumptions and very little go on with what you are doing. this could be done. 

function themename_preprocess_page(&amp;$variables, $hook) {
 if (arg(0) == 'newform') {
   $variables['template_file'] = 'page-newform'
 }
}