Two suggestions, sort of on opposite ends of the spectrum.
First: Practice doing "contest style" math problems. This helps your general math skills, and also helps get you used to thinking creatively and learning to gain some confidence in exploring your good ideas to their limit, while also encouraging you to quickly relinquish lousy approaches.
Second: Exercise. A lot. Whether or not you're already in good shape, you will almost inevitably find it hard to keep a healthy exercise routine when starting in college. So start building some good habits right away.
Re exercise: Good point, but I'd emphasize making a strong habit over doing it a lot. Spending a lot of time is easier during summer, but harder to carry over. Sure, do that, but also make sure you have a 15 minute routine, say, that you do every morning. Even a five minute routine isn't to be sneezed at, if you're doing bodyweight exercises like pushups.
Doing a stretch and 5 minutes of exercise during study breaks is worth a try. Could help avoid some of the physical problems with long hours of computer use. (Press down with your whole hand during pushups - strong fingers, hands and arms will help avoid RSI.)
This September I'll start college aiming for a computer science degree, and I want to use the summer for self-improvement. I'm very uncertain about what skills I should try to learn, though, and recommendations would help.