It is sometimes nice to stay just for the day after move in, just in case your student discovers the he would like/need something but it's not really necessary.
My experience with all 3 boys was that they got very busy very quickly, both with the "planned" activities, and with all the new people they were meeting, and really wanted us to disappear.
They are still in the high school mindset that being seen with their parents will make them seem "lame" to their new friends (none of whom, of course, have parents around who have just moved them into the dorm as well). And, of course, they are terrified of missing out on anything....
We stayed an extra day or two for S3 because we love DC. What worked for us was to have him text us a list of additional requests, and we ran out to the store and got the things he wanted. (he had forgotten his razor and a bulb for his lamp; wanted a small rug for by his bed and also wanted a second pillow; wanted some disposable silverware etc)
We arranged to meet him back at the dorm to drop stuff off and to see if he wanted to join us for a bite. He indicated that he did not want to leave campus, even though he was hungry--so we made mucho brownie points by picking up and bringing in a couple of 3 foot long sub sandwiches that could be shared with people on his hall. Instant friend maker.