I have been accepted to a Ph.D. program in St. Louis, MO and will be visiting the school in late March. I will be reimbursed for flight tickets. The scheduled Open House runs from Thursday to Saturday, and I have been told to book my flights with arrival on Thursday and departure on Saturday. The flight ticket per those specifications is at least $510, while if I arrive on Thursday and depart on Sunday, it would be $50 less. Since I will be committing 5 years of my life to studying there, I would like to know that I like the place, in addition to liking the Department (which I do). So is it okay to ask the secretary if I can book my departure on Sunday and save them $50 (lodging that extra night will be on me)?
Additionally, the secretary said they will book my hotel stay themselves. I would like to know St. Louis a little better, so I would like to stay at an airbnb place (which is more than 50% less expensive). Would proposing to stay at the airbnb place instead of the hotel they provide considered a strange request?