My daughter would not go on a public potty. In fact, she would hold it for HOURS after she first started the pee-pee dance, just so she wouldn't have to go. She would not go at church (even though those were TINY potties in the preschool room), or even if we'd been gone all day somewhere. What finally broke her was we picked out a toy together, and I put it on a shelf so she could see it but not play with it. I made her a little chart and each time she pottied in public, I put a sticker star on the chart. I told her she had to get 10 stickers. She would go a couple times on the potty, then boycott it, then go a couple days, then boycott. It took her about 3 weeks to earn her potty, and actually it was maybe 12 or 13 times, because I wanted to make sure she was really on the straight and narrow. :) We made a big deal of her EARNING her toy, and we did not have a single problem after that. The auto flusher scared her a little, but there were very few of those around us and she'd just ask me to hold her hands to catch her if she fell in. lol
Now my son was the one that couldn't reach the potty to pee pee. In public places, I would pick him up and let him stand on the tops of my shoes. This gave him about 3-4 inches, and we did this for an entire year PLUS. We never did cherrios, but we did give them each 1-2 m&ms for going #1 in a big potty (at home or elsewhere) and 2-3 for going #2.
Good luck!