This being the Bay Area, of course, you're never really that far from an earthquake or fault line.
As someone else stated, you should also be concerned about flood zoning and the quality of the ground below your house. E.g. the land under much of San Francisco is more prone to liquification in comparison a house on bedrock in Livermore because much of SF is landfill. Just the other day they talked about this on the local news, such as how the land under the million dollar homes in Moraga is like slush. I am like you, trying to find a place that has minimal hazards is difficult in the bay area.
It's important to define what you are comfortable as "close". When you look at fault maps of the Bay Area, the defined zone could be as narrow as 1000 feet wide. If you rely solely on an NHD report for your research, you could unknowingly be living 700 feet from the San Andreas Fault and not realize it.
Also, many NHD companies only review state maps and don't consider local maps in preparing their reports. Typically these are the less expensive reports. On the peninsula there are faults such as the Serra Fault and Monte Vista Fault that are not considered active (generally faults that have not ruptured within the past 11,000 years), but are considered potentially active. These faults are not included on state maps which only show active faults. Ute used the term "rated." Faults are usually rated as either active, potentially active, or inactive. The fault that runs through Auburn is considered potentially active and is mapped on Placer County Engineering Geologic Maps yet not on State Earthquake Fault Zone Maps.
If that's not enough to ponder, you should also be evaulating related hazards such as landslide potential, liquefaction, flooding, fire and even tsunami inundation when moving to the Bay Area.
A great site to research hazards in the Bay Area is http://www.abag.ca.gov/. Click "Environment" and "Earthquake Maps" and there are plenty of sources of information on seismic hazards in our area.
As a native San Franciscan, ex-carpenter and construction superintendent I can tell you that our buildings are built with full knowledge that the earth can move.
Remember that there are things that happen everywhere. Tornados, hurricanes, floods, fires etc. Be prepared to deal with what happens in your area and equip yourself with the knowledge needed to survive for the time right after the event. The priorities are to take care of yourself, then your family and then your neighbors.
When you buy a property in CA you'll get something called the Natural Hazard Disclosure Report ("NHD") which will show whether the property is located on or near a known earth quake fault. There are different kinds of earthquake faults. There are those that have already been rated and there are others that are only known but have not yet been rated. Chances are that you'll be either on or near an earthquake fault in the in CA. I work in Auburn CA which is not known for earthquake activity, but there's an earthquake fault that runs right through Auburn. It has not been rated, but it's still there.
You'll have a 3-day right of rescission after receiving the report. Thus, if you were to receive the report after the inspection period, you'd still have the right to rescind.
When you rent a place in CA, I think you'll have to probably buy the report yourself (cost anywhere from approx. $40 - $100 depending on which company you use), but you can also inquire with the county as I am sure they have pertinent information about earthquakes.
Check out this Nothern Callifornia Interactive County Map for the earthquake zones.
As kevin said, as long as you are in California, especially in the Bay Area, you are not too far away fron earthquake faults. I am sitting in between two faults - Roger Creek and San Andrea Faults.
The main thing is to be earthquake ready, including making sure your house is earthquake proof (from reinforced, bolted foundation to making sure all the pictures on the wall and certain glassware or displays are protected when the earth shakes -
A few companies in town prepare Natural Hazard Report with local information; a low cost way to find out.