There is no substitute for having actually done stuff. I have not and would never hire a EE that hadn't done a bunch of personal projects on the side. Electronic components are cheap and available, so anyone that has a true passion for electronics will have tinkered and built a few things, usually starting at least by late grade school. If you want to be a nuclear engineer, you can't get a kilo of plutonium and start messing around with it, but EEs have no such excuse.
These projects don't have to be pretty, don't have to work, and don't have to do what you originally intended them to. The point is that you did them because you wanted to, and hopefully learned something from them, and you have to be able to talk about them intelligently.
However, this is not something you should do because it will help you get a job. If that's your only reason, bail out now, EE isn't for you. In fact, if you're in college and you haven't already done some tinkering on the side, bail out now, EE isn't for you. I know that may sound harsh, but you seriously have to ask yourself why you want to be a EE. The right answer is that electronics fascinates you, you want to understand how circuits work and how to make circuits that do what you want. You are always thinking about ways to hook up available components, dreaming up things to build just to see them work and to be able to say you designed that. In other words, the right answer is that you have a passion for it. Anyone that has a passion for it will have done considerable tinkering, which will always be ahead of any formal education on the topic. When you do finally get to a electronics class, you already know all the basics, but occasionally you learn something that suddenly explains that puff of smoke you got when tinkering in high school, why that amplifier you tried to make from a few transistors just made a motor sounds, etc.
So no, there is nothing you should specifically go out and do to help get a EE intern job because if you are going to be a great EE you are already doing these things. If not, you're just kidding yourself. You might be able to squeak past some hiring managers that themselves squeaked past someone else. However, that is a short term gain at best. If you get someone that knows what they are doing, and you probably will, you won't be able to bluff your way thru the interview.
I once interviewed someone that had just graduated with a BS in EE from a local college. He brought his transcript and had impeccable grades. I think they were all As with maybe one or two Bs the whole 4 years. One question I always ask in a interview is to have you pick a project you have worked on and start describing it to me. Of course I don't know anything about your project, but I can tell a lot about how you think about things and how you present them. I'll ask questions how various things worked or how the design of this or that is. There is no way to bluff thru something like that. When I asked this kid about such a project, he said they hadn't done any in school. That's a little strange, but OK, so I asked him what he'd done on the side. I still remember his exact words, which were "What do you mean? That wasn't required.". Immediate end of interview.