Having a car will make visiting the marina and Indian Rock Park easier. However, a car will be more of a curse than a blessing for the campus and downtown.
Parking is significantly easier around Berkeley than it is in SF (but still far worse than South SF), so you can find a garage spot downtown for around $5 as long as there are no special events going on. Thus, I would lean towards driving since you already have a car on hand.
Keep in mind that traffic on the Bay Bridge can be quite bad any day of the week, so I recommend staying in the Berkeley/Oakland area until after 6 PM to avoid the worst of it.
There are so many places to go in the East Bay that it would be easy to fill a full day, making it easy to wait out the bad bridge traffic. I recommend a walk around Lake Merritt, for example, or a quick trek to St. George Spirits in Alameda for hard alcohol sampling. Also, Pyramid Brewery back in Berkeley is a popular stop and has tours every day at 4.
As someone who spends a lot of time in Berkeley, I would recommend driving, unless it is on one of the couple of Saturdays on which there is a university (Cal Bears) football game, when parking would be extremely difficult. You can get around most of Berkeley much more easily by car than by bus. That being said, like Dadaven said, it is very difficult to drive and park in or near the university campus, and parking is limited in the downtown (south Shattuck St.) area. If you were going to spend a lot of time there, or at the campus, you could park farther away and hoof it or take a bus (the most frequent are buses that run along Shattuck and University streets). Also, there is normally very heavy traffic getting back across the Bay Bridge from around 4 pm through 7:30 pm on a Saturday. If you were planning to return around that time, you might consider taking I-580 south to 92, and the San Mateo bridge back across the bay.
There is a Cal Bears football game both on Oct 11 and Oct. 18th, so this will definitely affect driving/parking. The times of the games are not announced yet. How about going on a weekday?
I think you might be confusing walking along Shattuck with walking alng Telegraph Ave, which is quite an experience and popular with visitors.
So game time on the 18th is 12:30. What time should we arrive to have any chance of getting a parking spot?
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