Getting "Permission Denied" when running pip as root on my Mac

Use a virtual environment:

$ virtualenv myenv
.. some output ..
$ source myenv/bin/activate
(myenv) $ pip install what-i-want

You only use sudo or elevated permissions when you want to install stuff for the global, system-wide Python installation.

It is best to use a virtual environment which isolates packages for you. That way you can play around without polluting the global python install.

As a bonus, virtualenv does not need elevated permissions.

Is it acceptable & safe to run pip install under sudo?

It's not safe and it's being frowned upon – see What are the risks of running 'sudo pip'? To install Python package in your home directory you don't need root privileges. See description of --user option to pip.