Propose modifications to a travel arrangement to visit graduate school 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?
It's perfectly acceptable to ask such thing, it does not make any difference to the department if you can show that the ticket price is the same or even less in your case. I suggest you try to stay longer if you can. When I was invited for an interview I was given a budget and I routed my flights the way I wanted.