Please don't live in East Palo Alto. It may have improved a lot over the past 5-10 years, but I still wouldn't recommend it.
Redwood City is a nice place to live; Palo Alto itself also has some affordable studios that fit in your budget. You can also look at Menlo Park. I grew up in and near these three cities, and enjoyed it. It's also international because of Stanford University and its location near silicon valley.
Another option would be finding a family that has a room to rent out; since the area is really popular with university students, there are a lot of families that do this with grad students. You might try searching for websites that have programs for that sort of thing, or perhaps Craigslist has listings like that.
I'd check Craigslist (
peninsula housing classifieds - craigslist) to get an idea for rent in different areas, but I'd highly recommend checking out different areas before you decide on a place for sure; neighborhoods vary in terms of the atmosphere, environment, type of peope living there... Apartment buildings often post signs indicating they have a vacancy available for rent. You can drive around and write down phone numbers to call (as sometimes you have to make an appointment to view a unit) or you can just stop by the office and talk to the landlord or manager.
Since you're coming from Germany, I'll assume you can't visit beforehand. Do you have anyone you can stay with for a few days while you find a place to live? Staying in a motel for a few days might be a good option, if you can afford it.
Also, be aware that internships are often unpaid; make sure yours is a paying internship before you accept.