I have competing offers, and I told departments that I'm going to their open houses. However, I am certain of which offer I want to accept. As this place is in a place with expensive living costs, I want to live in graduate housing, specifically, in an apartment style rather than dormitory style space. The housing application deadline is at the same time as the deadline to accept the offer of admission. I'm willing to commit to this school, but I've already told other schools that I'm going to their open houses, booked plane tickets, etc. I don't want to go back on that, but I want to accept my offer so I can hand in my housing application earlier.
Questions I have are: does handing in the housing application earlier affect my chances of getting the housing building I want? Will it be okay to submit it closer to the deadline, as in, will my chances get no worse than if I submit it earlier? Should I accept my offer of admission to this school of choice to hand in the housing thing earlier and cancel attending the open houses of the other schools? Is it unethical to accept an offer from one school but go to the open houses of others?