My bit of advice, albeit we did this many years ago now
, is to arrive the night before and stay in a hotel. Then, get up early and get down to the dorm earlier than they tell you to! Back then, the move-in started officially at 9 and they divided the day by alphabet. If they still do that, ignore it and arrive early. We were told to arrive at 9, that that was the earliest you could get in, etc. etc. Well, my D and her b/f went down by taxi at 7:30, and the rest of us followed around 8. By the time we got there, she had checked in, received her key, had been up to the room and was ready to move in. Cars can stop (depending on the dorm) right out front to unload, which means literally that you unload the car onto the sidewalk then go find a parking spot. Not that difficult, and the police there directing traffic can tell you several lots nearby.
Generally speaking, most people had someone stay with their pile of belongings on the sidewalk while the rest of their 'entourage' carried stuff upstairs. There were six of us so we got everything upstairs in two trips which was good because by this time, shortly after 9, the elevator line-ups were long (15-20 minute wait). After unpacking clothes, setting up bathroom stuff, making bed, setting up computer and tv, we went to K-Mart to pick up things we'd forgotten (sticky junk for hanging posters, duct tape, longer cable for tv and a few other small things). There was a welcome event for parents and that was that. If I remember correctly, the kids had an ice cream social event that evening with the kids on their floor.
One thing we did that in hindsight I wouldn't recommend is that we stayed in the city for a couple of days after that and my D joined us for a portion of that time. We should have left the next morning. The move in is chaotic, but it's a controlled kind of chaos.