Yeah, Craigslist makes it a little bit difficult because they don't do a mapping function. It is especially bad now that Craigslist and Padmapper are having a squabble (Craigslist isn't letting Padmapper list their offerings anymore). So it is hard to see exactly where Craigslist apartments are.
Here's my 2 cents for what its worth: in terms of safety, you should avoid the Fruitvale District (the murder rate there is pretty scary) and stick to northern Oakland and especially the hills (Claremont is really nice).
In terms of fun, Temescal, Lake Merritt, Piedmont and Rockridge are the best bets with the Emeryville area starting to really pick up lately. Of course, you should always go check the place out a couple of times before you commit. Crime is still high in all of these, but if you are street smart, aren't planning on joining any street gangs, and stay aware you can usually avoid trouble.
(Zipcodes don't really work that well, but plugging in the address into Google maps or even Padmapper will give you a sense of the place.) Good luck!
