I don't know of any area where you would be in the patient's room for 3 + hours, you would never have time for everything else that needs to be done.
In the ICU you try and minimize the time in the room, you go in, do assessments, give meds, monitor and then let the patient rest. Yes, when the patient is really sick and there is a lot going on you can be in the room for that long, but that is pretty rare. Trust me, you really don't want to be in the room that long. Exceptions are teaching, cluster cares, etc. Remember you will likley have 2 patients in the ICU and with all of the charting, coordinating other services, checking meds, charting, assessments, charting, charting, you would not have those three hours.
Since you do not have an offer for the ICU I would take the LTAC. It is a job.
Good Luck in your future as a nurse