If I call Tesla service out will they just replace the tyre or will they repair the puncture if they can?
My experience (in Sydney about 6 months ago) was:
* They normally send a service guy to swap your wheel to a swap one, you then take the flat one to a tyre place and get it repaired and put back on your car, then you call them and they come and collect the swap one.
* BUT when I called they didn't have any swap wheels available, so they then said they would flat-bed my car to their service place - which is a fair way away - where it would sit until Monday (it was Saturday afternoon) to have the tyre fixed there.
* Tesla's flat tyre service (ie the above two things) is only available for some number of km from a service location (might be 50km, might be 100km, I can't remember, not much in the scale of Australia anyway).
So I did what the posters above have suggested and was able to co-erce/bribe a tyre place to stay open for me to drive there (I went to a servo and gave the tyre a good top-up to get there) and have it repaired.
Some notes on this:
* They didn't have jacking pucks (I carry a set) so I had to show them and put them on (they only jacked one corner of the car with a portable jack).
* They had some trouble with the sound-deadening stuff inside the tyre. The apprentice who they initially rolled the wheel over to to plug it got stuck/confused and the boss eventually had to help him out.
* The day after this happened I took out NRMA road service for the car (on top of the included Tesla assistance) just to give myself less "flat tyre anxiety" as I drive a fair bit - not to anything like the degree that
@QBN_PC does but not small mileage either.