I would have to agree that Walnut Creek is the easiest to get to driving from Reno, is a nice area, and has easy access to BART. Lafayette is also a nice area and is just west of WC, and has it's own BART station.
You could take BART from any of the east bay stations into the city and get off at Powell to watch the start of the race at Union Square...
You could also stay somewhere on the peninsula (colma, ect.) as mentioned, and take caltrain and/or bart into the city, but as mentioned, that would be a little bit more of a trek than somewhere in the east bay.
I think the more difficult thing for you would be figuring out public transportation to Golden Gate Park (I assume that you would like to be there for the finish of the race). GGP is something like 5 miles away from the nearest BART station. I'm very familiar with BART, not so much with MUNI (bus/rail system). Muni does run to the vicinity of GGP, but I would recommend researching and familiarizing yourself with MUNI if that's what you want to take.
A quick trip search says walnut creek to Powell is just under a 40 minute trip, with a short 10 min walk to Union Square. ($4.85 one way per person on BART, 9.70 round trip) Then back to Powell, where there is a MUNI stop, and then a $2.00/person 1 way Muni trip to the area of GGP.
I'm not familiar with MUNI, but I do know that GGP is a big place, and I don't know where the MUNI stop in that area would put you in relation to where the race is going to end.
My recommendation would be BART to Powell/Union square, then find a set of cross streets that are walking distance to where you want to be in GGP and take a cab. It sounds like you only have 4 people, which will work for an SF cab (even the van cabs in SF will only take 4 people). A cab will be a little bit more expensive, $3.50 to get in, then $0.55 for every 1/5th of a mile, and $0.55 for each minute in traffic delays or waiting (SF taxis are not cheap). The advantage of a cab really comes in the fact that you won't have to figure out MUNI and they'll take you exactly where you want to go.
Good luck and have fun in the Bay.