If you are handy with a soldering iron and have access to basic components, I 100% recommend building a 555 timer/oscillator circuit.
I made my first of these when I was 13 or so, and it's dead easy.
Here are some links:
http://ourworld.compuserve.com/homepages/Bill_Bowden/page10.htm
http://en.wikipedia.org/wiki/555_timer_IC
Or, simply find a way to stress a length of piano wire (or steel cable) and use that as a simple resonator.
Or find a bit of pipe, drill holes, and make a flute.
Or make a pendulum (rather low frequency 'sound' source I admit, but a signal generator all the same).
I'd build a 555 oscillator, personally.
Cheap (5 dollars or less), portable, covers 4 or 5 orders of magnitude of frequency, can drive an LED or a speaker, wins hands down.