LORD KELVIN'S THUNDERSTORM:
Here's a simple (dirt cheap) apparatus which was devised by Lord Kelvin, about a century and a half ago. It generates high voltages in a surprising way, from gravity acting on drops of water!
The thing should be safe enough for a high-school experiment, but be careful not to touch both sides of the apparatus with two wet hands (you don't wan't any current going through your heart).
You need a reservoir of water (a 2-liter soda bottle pierced at the bottom will do nicely) which you can hang on a hook from the ceiling. Run two short hoses (or the two halves of one hose) so they receive water from the reservoir and let water drip (drop by drop, the flow MUST be discontinuous) at their respective ends, a certain distance from each other. The hose(s) must be made out of isolating material (rubber, plastic or glass tubing). Keep the outside of those tubes dry. Place two conductive rings (copper tubes, tin cans open at both ends, aluminum foil, etc.) around the hoses feeding the drippers.
Get two tin cans to collect the drops. Watch the cans as they fill slowly. You want to adjust the dripping rate so that there's always at least one drop in the process of falling (there's no point going more slowly than that). In fact, the dripping should probably be quite fast or else the instrument may charge up too slowly (or not at all, because of unavoidable discharging).
What do you observe? Well, nothing extraordinary at all ! You're not done yet...
Now, use electrical wire to connect, respectively, the left ring to the right can and the right ring to the left can. Make sure the connecting wires never come too close from each other.
What do you observe now? Well, still nothing much at the beginning but something quite spectacular happens after a short while: The drops will "refuse" to fall into their respective cans. They may even "explode" into fine mist and make a wet mess all over the place...
What is happening? Well, I don't want to spoil it for you, but you may want to consider that the electrical symmetry of the apparatus is unstable... If one half of the apparatus gets slightly positive and the other slightly negative, the difference will only increase in the same direction until Nature refuses to proceed any further and does something "funny" to prevent that unbounded increase.
To "jump start" the process faster, it may be useful to approach one of the cans with an electrified object, but this should not be needed.
To the best of my knowledge, this experiment has not been done in an high-school context yet, so you might be breaking new ground, so to speak... Good luck.
The first link below is to my own site. It does not contain any information about this experiment (yet) but I am willing to go into more details and/or report your own struggles and "debugging" of the experimental setup if you decide to go ahead with the project. (You'll find my e-mail address near the top of that page.) If you do it, I'd like to hear about it!
The second link seems to include useful experimental tips. In particular, it includes an idea for emptying the cans without discharging them if you want to run this electrostatic generator continuously by replacing the top reservoir with a hose connected to a faucet...
This experiment can be as simple or as refined as you care to make it.