That said, I don't think crime is the main reason to not live in the East Bay when you are doing an internship. Minimizing transport time to work and/or recreation is why you don't want to live out there. If you are working in SF, live in SF. If work is in the south bay, live in the south bay...or maybe live in SF. It will be expensive but an internship should cover it. If the internship doesn't cover it you picked the wrong internship.
The most important thing is to live near other interns. If everyone's in the city, live in the city. If you want to get a house with a few people, or just prefer a more laid-back vibe, the East Bay is a great option.
As for the crime in Oakland, some guy got shot in front of his own house in the Mission this morning. People arriving for their internships, not being familiar with SF neighborhoods, shouldn't get the impression that the Mission is some kind of picnic.
If you're working in the South Bay, yeah, don't live there. But Temescal, for example, is a great option if you're working in the city. Great city feel, lots of cool stuff, and you're still only 20 minutes from the city. That's a shorter commute than many parts of the city itself. It's expensive my national standards, but still cheaper than the city.