How do I determine the range of my ships? I can't find anywhere where it is displayed.

The problem is I need want to place an outpost or two to extend the range my ships can travel to so that I can check out some extra planets, but because I don't know what the range of my ships is anyway I have no way of knowing whether placing the outposts will even enable me to reach the planets in question.

Am I missing something obvious?

Indeed it is not that obvious in MOO2.
You need to know which fuel cell technology you have.
Check it in INFO / Tech Review / Equipment / section: Fuels/Range.

Say you have just the basic Standard Fuel Cells, they will give you 4 parsecs range from your Colony or Outpost.
If your ship has Extended Fuel Tanks, you can add 50% range.
Colony and Outpost Ships always have Extended Tanks fitted.

You can check the range between stars by using F9 on the main galaxy map.

Perfect, thanks very much. :)