Is there a way to constantly show my external IP address in the top unity bar?

Taken from this GitHub project here is a decent indicator that might help:

Installation

PPA and install

sudo apt-add-repository ppa:bovender/bovender sudo apt-get update sudo apt-get install indicator-ip

This will install the program and configure automatic start at login. To run it right away, press ALT+F2 to open the Unity command prompt and enter indicator-ip.

Try installing conky. It's an extremely configurable app that can be integrated into a desktop to show lots of information. There may be an extension out there for a section to pave onto a tool bar. http://conky.sourceforge.net/documentation.html