[mjb]

Starting with something like a GNU Radio board (http://gnuradio.org/) and a commercial antenna, you could put together a basic CW or ICW radar in a weekend without too much trouble. A little bit of care is required to not break any local laws or piss people off.

Simply, you would send out a radio signal, bounce it off a target and measure the time between when you sent the signal and when it was received. That delay is inversely proportional to the speed of light. Take a bunch of samples to integrate away short term clock inaccuracies (but don't integrate too long, because some types of clock noise will make your answer worse and not better) and you'll get a pretty good estimate of c.

Another GNU Radio based experiment would be to attempt to pick up multipath reflections of TV or radio broadcasts off large geographical features or buildings. Basically, you would capture two signals - a direct version of the broadcast and a delayed version. The errors would be large, but you would be able to get fairly close to a reasonable estimate of c (in air).

Before doing either of these experiments, mocking them up with a speaker and microphone or two ultrasound transceivers is a good idea and will save you a bunch of time. 40kHz is easier to work with than 2.4Ghz for sure.