Unadjustable public barbeques with a drainage hole in the middle. Any thoughts on what best to block this hole with? This if for times when I dont want oil/fat to drain away, not vandalism. Any other tips for cooking on these things welcome.

I used a small inverted terracotta plant pot once. It worked well.

cork?

im pretty sure it wont burn away

or you could try a whole bunch of napkins rolled into a tight roll. it should stop most of the oil from draining away, and is disposable.

I presume you're referring to the ones that take charcoal briquettes. Don't know why you'd want to save the fat/grease there, because it'd be unlikely to make it that far anyway, since it'd likely burn up on the coals. If you did manage to save some, I'm sure it'd be full of ash and pretty well broken down due to it being exposed to heat for so long. You'd wind up with a big, sticky blob of carbon.

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"Never try to teach a pig to sing. It wastes your time, and it annoys the pig." --Robert Heinlein

The napkins will absorb the oil and create a big candle wick. Not the greatest idea.

A large ball of napkins under charcoal briquettes covered in grease...

This sounds like the behavior of a drunk uncle at the family get-together in the park.

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"Never try to teach a pig to sing. It wastes your time, and it annoys the pig." --Robert Heinlein

Actually I'm referring to propane ones, but thats neither here nor there.

The actual "why" for this is to emulate baked vegetables - I've tried it, and it works, but the oil draining away is annoying. On further thought I'm thinking two layers of foil folded at the edges should work, with the advantage of not needing to clean the barbeque as much.

The ones like you mention, around where I live don't get super hot anyway.
I could imagine a potato carved to the right shape to fit in and act as a plug would do the trick, and it might even be edible afterwards too.