IMO public trans is terrible in southern california unless you plan on staying seeing things directly on the coast.
San diego especially is not good , uber is your best bet .
Look up the "coaster " and "sprinter "  amtrak to give you an idea how the trains in san diego run. Personally i wouldnt ride the bus .
LA has a mini subway that runs from the westside "coast" to west hollywood to downtown but thats it.
They also have services like zipcar? that let you rent cars hourly , they are parked randomly over the city.
California is a driving state , i think some of the best things you will find will be when you are driving around randomly , drive the coast highway PCH

@heavygenes gave a nice list of stuff . i might add that shopping for men is not so great although your wife  might like it . Cool stuff out here for kids depending on what they are into.
As far as breweries there are a ton of good ones , might want to look into the pub crawl tour things they have going on now.
Gaslamp (downtown) in general is good for sight seeing ,bars  and food .
Los angeles is great but plan your trip wisely so you don"t fight the traffic , staying central to the location where you plan sightseeing in la is crucial as its spread out and driving alot will take the fun out of it.
Would also recommend Tijuana if your kid is older than 12.

thanks @nny1 fast shipping and great item