I second the recommendation to live within near a BART station. (Okay, you can also drive to BART, I suppose.)
Piedmont is an upscale white enclave within Oakland. That's not good or bad - just a fact.
Oakland also has some decent and livable neighborhoods, but you'll need to check them out very carefully.
Albany is nice enough - like a lesser version of Berkeley. As with Berkeley and El Cerrito, you can find quieter neighborhoods or neighborhoods within walking distance of cafe, shopping and a downtown drag. You can also find sketchier neighborhoods.
Hercules has a much more suburban Americana feel - newer, with much bigger and "nicer" houses, but altogether missing character of a city.
Definitely check out DSE runners.
With two kids, you'll want to check out the school district. District, and individual schools, vary HUGELY. California public schools are underfunded and in trouble. You can find the occasional good or excellent school, but you may have to consider private schools. My guess is Hercules has the best schools on average of the cities you mention ... but it's boooring.
Albany is not far from UC Berkeley.
Also consider the Rockridge neighborhood of Oakland.
Oakland hills and Berkeley hills are gorgeous, but then you are totally car dependent for everything.
Check out sfgate.com, sfist.com, weekendsherpa.com.
Welcome to the Bay Area! It's awesome.