I have 8 children and have been in a waiting room (or stuck at some other unforeseen place) a time or two with a toddler. In fact, often with several toddlers at a time. I found that these situations were not just the regular-boring-kind but the outburst-boring-kinds for kids.
One of the things that worked for me was the Mini Kid Kit. It was just a small bag in my purse that had travel size things, (tiny flashlight, metal play keys, mirror, bracelet, heavy necklace, hair clip, etc), items they never got to play with under normal conditions. Basically, anything that they were curious in and weren't allowed to play with; or small toys that they usually couldn't touch because they were "mine", kept their interest when they were outburst-bored in a public place. It helped to keep them quiet on many occasions.
This helped me not become the outburst mommy of the outburst toddler. If I felt like there was something in my power to do I became less frustrated and more in control of the situation. Toddlers, especially on the verge of tantrums, definitely need a mom in control of herself and the situation. The Mini Kid Kit was a tool for me to do that.
But there are 3 keys to the Mini Kid Kit
1) You don't give the child the whole bag, bring out items one at a time
2) They don't see the bag in its entirety so they don't fuss for the next item before they've explored the first
3) You take away the toy (and give them the next one) before they get bored with it
Rotate and re-rotate them around.
Hopefully, this little tip will help you. Go ahead. Grab a ziplock bag, add a few things in it, and put it in your purse. Done.