React.js, wait for setState to finish before triggering a function?

setState() has an optional callback parameter that you can use for this. You only need to change your code slightly, to this:

// Form Input
this.setState(
  {
    originId: input.originId,
    destinationId: input.destinationId,
    radius: input.radius,
    search: input.search
  },
  this.findRoutes         // here is where you put the callback
);

Notice the call to findRoutes is now inside the setState() call, as the second parameter.
Without () because you are passing the function.

       this.setState(
        {
            originId: input.originId,
            destinationId: input.destinationId,
            radius: input.radius,
            search: input.search
        },
        function() { console.log("setState completed", this.state) }
       )

this might be helpful