The people responding are being douchebags - My girlfriend and I survive making less than 40k each, and moved here in January. It's not impossible to survive and enjoy yourself here while making less than 100k. Especially with three folks total, each making 50k, you're better off than you think.

However, for 3k or less on a 3br, you aren't going to be living anywhere explicitly interesting or fun...

Is your work BART accessible? That makes things much easier, because the freeways between Oakland and San Leandro are way beyond capacity, to the point of ridiculousness.

I would browse padmapper and look around. I'm only really very familiar with the peninsula, so since you'll probably be in the East Bay, I can't help much. Here are some of my impressions, though:

SF - Expensive, Fun, Expensive, expensive, and expensive. Not exactly livable unless you make a crazy amount of money. Don't bother looking here.

Oakland - Expensive in parts, cheap in others, rapidly changing. There is a crime problem. Some neighborhoods can vary wildly street to street. I live in Oakland and I love it. Do your research, and you can find some real pieces of gold. I landed on a piece of gold and beyond the short bus ride to downtown/BART, everything else is great.

Berkeley - A bit further north, I wouldn't live here unless your work in on BART and you can somehow find an apartment near BART, but this place is also crazy impacted and full of students.

I was born and raised in San Mateo, and although areas on the peninsula like San Mateo can appear to have somewhat sane commutes to the East Bay using one of the bridges, just don't. Don't even think about it. Those bridges, too, are so amazingly over capacity that it's almost funny.