Restaurant recommendations for East Bay California?

Clearly I'm going to need a longer trip. Thanks all!!

I must chime in about Fenton's Creamery on Piedmont Avenue, where we have been enjoying Swiss milk chocolate milkshakes ever since college...38 years ago...oh my! They also have delicious crab sandwiches. Last time we were in the Bay Area we went to Chez Panisse for lunch and, unfortunately, were disappointed.

Another thought, a stroll through Oakland's Chinatown district on a weekend morning is very pleasant. It's close to the Marriott/Convention Center. There is a Saturday farmers market just outside the convention center doors.

I know people still love Chez Panisse but the best "grown up" restaurant in the East Bay is Oliveto. It's just across the street from the Rockridge BART station which is practically the boundry line between Berkeley and Oakland.
Not in Sonoma but not far, Thomas Keller's Bouchon in Healdsburg. It's just down the street from his French Laundry. Unlike the French Laundry it's a zinc bar type place which serves trencherman sized portions. It's a shame that Copia no longer exists.

For the adults, Chez Panisse is still a treat after all these years.

If you want seafood, Horatio's in San Leandro is great.

For Sonoma winery, check out Arrowood Winery. Really nice unpretentious people.

Burma Superstar (a long standing favorite in the inner Richmond in SF) recently opened a second location, on par with the original, in the Temescal neighborhood of Oakland. It gets noisy and you have to wait for a table later in the evening, but if you go early might be good with kids. Really spectacular Burmese food.

Gelateria Naia in downtown Berkeley makes great gelato and sorbetto in a cornucopia of flavors, with samples freely and cheerfully dispensed. My favorite is a cup of pistachio gelato and fig sorbetto.

I second the College Ave and Market Hall rec's. La Farine, a bakery on College Ave, is a favorite of mine, especially their morning buns, rye raisin rolls, and rustic baguettes.

In Sonoma, I've particularly enjoyed wines at Unti, Eric Ross, and Frick.

This isn't food related, but you might want to reconsider heading into SF for the Hardly Strictly Bluegrass festival in Golden Gate park. It has a really diverse and excellent lineup and it's free, endowed by a SF financier.

Adding on to what AJ said, you might consider a walking/stroller "tour" of College Avenue. Cactus and Market Hall are right next to BART, if you're taking public transportation, and there are lots of great options going either direction--restaurants, cafes, chocolate, ice cream. And bookstores and other places to visit along the way.

Toddler friendly favorite (which we love going to, even now that are kids are grown) is Cactus Taqueria across from the Market Hall at Rockridge. (The Market Hall is fun to wander through.) Easy parking in the lots across the street under the freeway, especially on the Market Hall side, in the evening. Evening out: We really liked Homestead, a new place on Piedmont Avenue. Excellent chefs, small but nice menu, house-cured (really tasty!) charcuterie, thoughtful condiments, open kitchen, good food, quite reasonable. If you can swing "adult mid-day out" out, go to Chez Panisse! (I prefer the place during the day.) Get a booth or table near the open kitchen. It's one restaurant that is consistently as good as it's cracked up to be, seriously. Plus, it's of historical importance, from a culinary perspective. ;o)

You are coming to food heaven! I'll start: Camino in Oakland is one of our standards, and you can usually get in at the last minute. Not really a kids place, but if your toddlers are used to eating out, they can go.