From my recollection, most of the major airlines don't jack their fares until about 2 weeks prior to the flight. However, by this point you may get screwed into an inconvenient itinerary: this is the most-lethal complication of air travel for interviews, for if you have this trip back-to-back with another, and you get screwed out of the latter because of poor planning, then you'll be faced with having to possibly cancel one of them. And, since it is a recurrent theme here that "more interviews tends to be a better idea for matching", it would seem that you should try and maximize your logistics for travel.
So, all things being equal, if you'd even consider working for your fly-a-way institution, go ahead and book your tickets for a schedule you like. You may ultimately have to shift the closer interviews around, but you can do this.