Hi Silvercat,
If I am eating in a restaurant then my personal choice is to take the pack to the toilet and inject there. Usually restaurants have pretty decent toilets, and if you find their toilet looks like a public convenience, then I would say that reflects on their standards of hygiene and do you really want to eat in somewhere like that!
I guess I would be a little embarrassed to inject in public, but as well as that, before I started on Byetta I was very queasy about needles and injections, to the point where I had been known to pass out at the sight of an injection. Whenever I had needed one, for tetanus or whatever, I have always had to look the other way. There must be others out there like me and I wouldn't want to inflict that on them.