Best location for Craft development? Local or Server? Subfolder of production?
The best way to do it would be to develop locally, ideally managed with a version control system like Git and then push your site to your server. Craft handles a multi-environment workflow very well.

From the Craft docs on Mult-Environment configs

A good screencast from Straight Up Craft

There are also several questions and answers dealing with this topic in Stack Exchange here.