The correct answer is : While looking for a campsite,a tornado touched down near the park.
By definition, a dangling modifier comprises a phrase or clause whose relationship or link with the word or words that modify is well and clearly established.Typically, the dangling modifier appears at the beginning of the sentence.
In this example, the dangling modifier appears at the beginning of the sentence and it fails logical reference. That is to say, it is not logical to think that the tornado was looking for a campsite. In this case, there is no reference of who did the activity of looking for a campsite.In other words, there are no specific word that this clause modifies.