The first chapter of the game, there is one public quest, each chapter after that there are three public quests. So there are over three hundred public quests in the game. That equals quite a few per zone. You will find public quest pretty much everywhere as you go through.

As you get into later stages of the public quests, it requires more and more people, because the encounter becomes more and more difficult and complex. So you will still be able to participate and gain influence in public quests if you are by yourself, even if you can't complete it by yourself.