Ooo...where shall I start! I lived in SF for 2 years and it a wonderful city. Admittedly I didn't have children at the time so I'll try and temper my view a little! A word about the weather. SF can actually be quite chilly. Even in the summer make sure you have a jumper with you all the time. Especially bad time for the fog. Autumn/Spring are the best times of year to visit weather wise.
Firstly, Americans love children. They won't even blink if you take them to posh restaurants etc. and you should find no problems with high chairs, changing facilities etc. You'll find childrens meals in most restaurants although you may get a bit sick of the 'fries with everything' approach.
Places to go outside SF:
Yosemite is amazing. Can't rate it too highly. The most breath taking scenery I've ever witnesses. However, it's a long drive away. (5 hours or so if I remmeber rightly). Stunning scenery. Loads of places for the kids to run wild. Lots of walks (if you're into exercise) and guided 'train' rides (on carriages pulled by a tractor) if you're not. Should be places to hire bikes if you're into that.
Tahoe - Again a fair drive away (5 hours or so) but it's beautiful up there. Lovely walks and big lake. (You may even catch the last of the snow if you fancy a quick ski although it won't be the best quality snow).
Calistoga - North of SF. famous for it's sulphur spings. if you can get a few hours away from the kids try a mud bath. Smelly but very relaxing.
Napa - Again North of SF. Major wine region. You can go on a wine tasting trip by just driving from one vine yard to another. Most don't charge for tasting and normally have a non alco grape juice that the kids could 'taste'. Best bit is you don't even have to buy any wine and can get quite sloshed! (So make sure it's someone elses turn to drive...They're very hot on drink driving and on speeding in California).
Muir Wood - Just north of SF. It's a protected area of redwood forest and has a lovely trail and, I believe, they do guided tours with the park rangers. Best bit is that the park rangers look just like the one from Yogi bear!
Great America theme park - A small theme park by American standards but it still puts Alton Towers to shame. It's down the bay, Santa Clara/San Jose way.
Beaches - I forget the names of the beaches but if you head north of SF again and turn left you'll hit some lovely golden sandy beaches. Also, you could always head for Santa Cruz. Golden beach and tacky boardwalk with mini funfair.
Things to Do in SF (Apart from shopping!):
Golden gate park is a must. there's a boating lake and a carousel, plenty of room to run around and, especially at the weekend, all the cool San Franciscans hanging out on their skates. You can hire bikes/skates and try it out yourself! (How's your balance?).
Almo Square: Small park with stunning views of the city and lined by the 'painted ladies' (old typical san franciscan houses).
Cable cars: Great fun. More expensive than the buses but has to be done. Try out the cable car museum too. Last time I was there it was free.
Ghiradellis: Sure I've spelt that wrong....Really tack tourist trap but good ice cream sundaes.
Pier 39: Again a tourist trap. Normally to be avoided but the kids might like to see the seal lions that have taken over part of the area.
Alcatraz: Excellent audio tour. probabaly not the best thing to do with the kids but they might enjoy the boat trip over to the island.
Coit Tower: Nice view. Don't waste your money paying to go inside though.
Lombard street: So it's a wiggley road. Big deal. Not worth queuing to drive down it.
Embarqadero (sp?): touristy shopping but quite nice and they may have added some attractions for the kids. Has a cinema (movie theatre!) there as well....Maybe you can see a movie before it's released back home? They have a skating rink there in winter but it's probably not there this time of year.
China town: Busy but really interesting. Not sure that the kids will enjoy it much though but you have to check out the weird and wonderful things they sell in the food shops.
Exploratorium: A must for your 6 year old (and the 2 year old should be amused too). A science museum done American style. Lots of knobs and buttons and levers etc to play with.
Things to eat:
SF is a wonderful mix of cultures. They have the best Thai food I've tasted anywhere and very authentic Chinese. Not to mention mexican and your typical American Diner. Book a diet for when you come back....and don't bother with starters unless you're planning on sharing a main course as the portions are huge.
Ummm...I'm sure I've missed loads....I'll post again if I think of anything else!