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The Bay Area is one of the most expensive areas in the country for housing. The cheapest places in the immediate vicinity will be either Richmond or Oakland, although the cheapest neighborhoods in either place are not very safe. I would suggest using bestplaces.net and look up the crime rate by zip code (this isn't precise, as something like neighborhoodscout.com, but that is kinda expensive).
You're best shot at finding a really great deal for the summer will probably be as a subletter; that is, a student who has an 12 month lease who will be gone for the summer. The best resource for that is probably Craig's List. At least where I'm currently attending school, you can sublet Jun-Aug for about the cost of what the unit would cost for a single month (sometimes they're even furnished). But it's something that can be difficult to arrange from a distance. Do you know anyone in the area who might be able to vet prospective places for you?
Also, one piece of advice about sublets: don't pay in cash. Pay with a check or money order and note in the "memo field" something like "Sublet <Address> for Jun, Jul, Aug of 2011" or whatever. I do know a few people who have paid in cash and then have gotten burned, particularly when there's not a formal rental agreement.
In terms of Berkeley Extension, they offer two types of classes:
1) "Extension Courses" that are taught exclusively by Extension faculty exclusively to Extension students;
2) Take real UCB courses as a visiting student (or sometimes called "continuing education"), be graded on the same scale as Berkeley undergrads, etc.
The latter is worth your time; the former will not provide a lot of signal value for admissions because adcoms know that its not a true Berkeley course (it's a cash cow and is akin to a community college course). When I took some time off as an undergrad to work full-time, I took a few Extension courses and was very disappointed in the instructional value and I don't think the school that I transferred to (another UC) awarded transfer units for those courses. IMHO, they're not worth your time or money.