Here's a completely not comprehensive list of some local points of interest and things to do, including a few of our favorite places to eat, and some ideas for things to do if you're bringing kids along.
If you want some more comprehensive guides, the San Francisco Chronicle Guide to Easy Bay Neighborhoods may be a good starting point.
The wedding site is only one part of a larger park that has a swimming pool (Clarke Swim Center, (925) 943-5856), tennis courts (Walnut Creek Tennis Center (925) 945-0105), playground, and more. For more details, see here.
There's also an outdoor public pool right around the corner from our house, the King Swim Center at 1700 Hopkins, (510) 644-8518.
The Lawrence Hall of Science is a science museum not too far from our house, up in the Berkeley Hills. If you're willing to trek across the bay to San Francisco, the Exploratorium is an excellent science museum for both kids and adults.
There are lots of parks in the East Bay hills, with plenty of opportunities for hiking. See the East Bay Regional Park District for more details.
Or if you'd prefer to stay at lower elevations, consider a walk along the water at the Berkeley Marina.
Or if you want a more unconventional and unique waterfront experience, check out the artwork at the Albany Bulb. A few related links include this, this, and this.
Across the bay in San Francisco is Golden Gate Park.
While our favorite Thai food is either what we get in Thailand, or make ourselves at home, there are indeed plenty of good Thai restaurants locally. A couple in Berkeley are Plearn and Cha Am, but that's just the tip of the iceberg. It's hard to throw a stone and not hit a Thai restaurant, and more often than not they're good.
And although it's not necessarily the best Thai food ever, you will get a somewhat unique experience at the Thai Temple Sunday Brunch. If you go, don't miss out on the little coconut milk pancake like treats (I have no idea what they're really called). This is the only place outside of Thailand where we've ever seen them served, and they're quite tasty.
Le Cheval is a good higher end Vietnamese restaurant in Oakland.
If you're staying in downtown Oakland, there's a good place for cheap (about $2.50) banh mi (Vietnamese sandwiches) somewhere in Chinatown, I'm pretty sure on Franklin between 8th and 9th Streets. Actually, there's plenty of good (and often cheap) places to eat and shop in Oakland Chinatown, if you're looking for something interesting near the Oakland hotels.
There's probably as many (or more?) Indian restaurants as Thai. A few worth mentioning include:
There are a bunch of Ethiopian restaurants along Telegraph Ave. in both Berkeley and Oakland. Generally quite tasty, but only go if you're not in a rush.
Zachary's - An experience if you like deep dish pizza. Although it's not really the same thing, it's actually stuffed pizza. Note that it's cash only.
But if you like thin crust pizza, you should check out the Cheeseboard pizza collective. Two doors down from the regular Cheeseboard. Rich didn't really like thin crust pizza until the Cheeseboard. If you're in Oakland, there's Arizmendi in Emeryville, which is part of the same co-op, and is still good, but not quite as good as the original.
The actual Cheeseboard just sells bread and cheese, and is the best cheese shop we've ever seen, by far. If you're into cheese, you really should try to find the time to check it out. You can taste anything you want.
If you are stopping by our house and want a quick coffee or chai or pastry, we really like Espresso Roma, the coffee shop around the corner. They have the best croissants we've found in the bay area.
Our favorite pub in Berkeley is The Albatross. They also have darts, and a bunch of board games available for loan.
Two good brewpubs in Berkeley are Jupiter (which also has free live music outside) and Triple Rock.