If it were me, I would fly out the evening before, get a room at the Sheraton or Alt Hotel and have a nice lie in the next morning. If you have most of the day, I would be tempted to take the UP train and enjoy the morning in downtown. I have stayed at the Alt a few times and it is quite pleasant. I have not stayed at the Four Points that is also walkable from T3 but it is often less expensive than the other two hotels I mention above, so that may be of interest. If you are wanting the morning flight, isn't that at something like 5 a.m.? That would ruin the night for me anyhow, so an extra incentive to just go out the evening before and get a good sleep.