I took my own tools off to college. It was in one of those lunch boxish sized single removable tray plastic tool boxes. My tools were generally not going to work for automotive fixes other than pulling the radio out since that needed only screwdrivers.
I was more likely going to open up a computer, or home electronics/stereo etc. Screwdrivers, both regular and precision sized, slip joint pliers, needle nose pliers, basic soldering iron and supplies, very basic-compact multimeter, crescent wrench, hammer. That was about it. If he is going to have a bike on campus I would get a few tools that will help him service/oil it. WD-40 isn't supposed to be chain lube but after my chain rusted solid from a ice storm it sure did help! A tire plug kit and 12V compressor for in the car is something I would also really recommend. I also might suggest telling him how/where to buy tools if needed. For example, at one point in school I needed to fix the heat controls in my car. One of the pull cable housings broke free of it's mount. I needed a 10mm socket to get that part out. I don't recall where I bought the socket set but they were total ****. These days I could probably buy something sufficient from Walmart for $10 or something from their Hart line for $30. Since, in college I really didn't need socket sets I would suggest not getting/taking any unless the need comes up.