A navigation system would be unusual in an American rental car below premium or luxury level. Many (probably most) of these cars are special ordered from American automobile manufacturers and they are bottom-of-the-line with respect to optional equipment. In some cases, they have fewer features than the cheapest model available to the general public. Frankly, I would suggest Google Maps is just as good, especially because I know Google Maps is tied in to the traffic reports. Rush hour traffic in the USA and in particular in the San Francisco Bay Area may be more crowded than what you are used to. SF is on a peninsula, and the bridges are packed solid at those times. There are special carpool lanes marked with a diamond for vehicles with at least 3 (to/from the Bay Bridge to Oakland) or 2 (other highways) passengers. You may drive your rental in them, if you have enough passengers.
All major rental car companies include roadside service, in case of a flat tire or mechanical failure.
The rental car company will offer you (for a fee) use of a transponder to pay tolls on the bridges. It is called a "Fastrak", and also has special lanes. (The carpool lanes at the toll gates always require Fastrak, but not conversely.) The queue can be much, much shorter than the cash-payment lanes. The Golden Gate bridge is now electronic payment only. The transponder fee is, of course, in addition to the tolls, which range from $4 to $6 and are charged in one direction only.
At SFO, all rental cars are kept at a site some distance from the main terminal. There is a new monorail to the Rental Car Center. As Aleks says, decline the option to return the car without fuel. Simply fill the tank on your way to return the car. There are many stations quite close to the Rental Car Center, and they charge much less than the rental company.
I don't know if you have driven in the USA before. Remember to use miles and not kilometers. Your speedometer, if analog, will be marked with both. Second, we have been slow to adopt international signage. Third, be especially alert to parking restrictions, which will be only in English and are sometimes complicated. Yellow curbs are for parking of commercial vehicles only. Red is a no-stopping zone. White is a brief stopping zone to get in or out of a car, usually at a building entrance. Green is a short-stay zone, 15 to 30 minutes as signed. Downtown spaces have parking meters, and are as high as $4/hour. Don't worry about needing massive amounts of coins, most of them take credit cards. (Caveat: I don't know if they will take European chip-and-pin cards.) Except in parts of San Francisco itself, parking regulations other than red and white zones are usually turned off at night and on Sunday.
Right turn on red light originated in California and is usually permitted, but if not, the sign is usually in English only. (Sometimes it is prohibited only during the day, and OK at night.) Green left turn arrows indicate that the oncoming lanes still have a red light (protected turn). Compulsory turns from lanes are indicated with black on white signage; the international white-on-blue is unknown here. The indications are usually also painted on the street itself. Pedestrians have right of way. Be alert for striped crosswalks (British call them zebra crossings). This is theoretically true in many places, but is enforced in San Francisco.
Do not leave valuables visible in your car when parked. This includes hotel lots.
Don't hesitate to ask if you have other questions.
