I accidentally installed a wrong version of wxPython (3.0.2.0).
When I try to install the latest wxPython-4.0.1, I get the following error:

Found existing installation: wxPython 3.0.2.0
  Cannot uninstall 'wxPython'. It is a distutils installed project and thus we cannot accurately determine which files belong to it which would lead to only a partial uninstall.

So, I searched around a bit and apparently you have to use the uninstaller found within your original wxPython-3.0.2.0 dmg file in order to uninstall it. I did not have the file anymore it seemed, and went through my history to get the exact download and version from Sourceforge (I think!), but when I use the uninstaller, I get the following:

* No wxPython installations found!  *

How am I able to remove this old version of wxPython?
I am very new to this, so sorry if this sounds stupid.
Thanks!
As you've discovered wxPython Classic and wxPython Phoenix use different installation strategies. In fact, Classic's approach is quite messy compared to Phoenix's, the uninstallation script was created to help to undo some of that (especially the things left behind by the OSX Installer tool.)
The good news however is that you can manually clean up the parts that pip is complaining about. I don't have it installed here any longer to be able to give you exact instructions, but from memory it should be something like this.

In your Python's site-package folder, (something like /Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages) remove folders and files starting with wx.
In /usr/local/lib remove any folders starting with wxPython

Additionally, wxPython Phoenix is not required to be installed globally like Classic was. If you use virtualenvs or Python3's venvs then you can install the wheel in them instead of your global Python environment if you prefer.
Cannot uninstall wxPython 3.0.2.0 (macOS)?