No, no public transportation (any good one) in Benicia. There are a lot of groups that meet and car pool, and do ride sharing, though.. Here is a link to find one:
http://www.carpoolworld.com/
I bet you can also find one through Craig's List. The commute to Hayward from Benicia, would be terrible, especially coming back to Benicia during commute time. You are looking at at least 45 minutes to and an hour or more coming back, in good traffic.
The drive to vacaville (which is actually I- 80) would be ok, about 45 minutes. I think most people are coming from the fairfield/vacaville/sacramento area to work in the bay area, rather than the other way, so that traffic shouldn't be too bad.
You might be better off living closer to hayward, since your commute won't be fun.
I've lived in Benicia, my whole life, and can say it's a great place to live, and raise a family. It is getting expensive to live here though, now because of this.
Good Luck to you!