I personally never ride Muni. It is dirty, runs people down and is crime ridden. There have been a rash of robberies of young thugs snatching peoples iphones, itouches, ipods or blackberries. Not to scare you but you need to be aware of this. Some crazy people ride that bus! Be aware of your surroundings.
BART is good if you are just doing the financial district but don't get off on the Market station. WAY scary!
I respectfully have to disagree about Muni. I rode Muni both by bus and by "muni"(train) everyday for four years and never had a problem. This was from ages 18-22, being a young white female. Sure, bad things can happen, as they do in any major city. But I truly believe that it's safe for tourists who keep their wits about them. Main tips are: Be respectful of other's space, keep your children by your side, and try to have a good idea of where you are going before you board the bus. Myself included, I have seen many people on muni who are happy to help tourists with directions/or when to get off.
I think that the main problems with Muni have to do with riders who take up more than one seat with their bags, and those who are completely unaware of their surroundings(i.e. headphones on and oblivious!) As the previous poster said, Muni has a history of hitting pedestrians, but so do many SF drivers...so look both ways when crossing the street, and please don't try to catch the light when the red hand is flashing.
One last thing, the Market Street/Powell station is not scary in the least. All of the exits will put you in safe areas near major shopping outlets and tourist areas. In fact, the Powell station filters directly into our beautiful new mall, with Bloomingdales as the flagship store. I highly recommend this station, as you can transfer easily to the Powell Street cable car. Train stations to avoid would be Civic Center and Van Ness, as they are not tourist type areas(albeit City Hall).
Now, some ideas..
***Take the "L" Train out to the San Francisco Zoo and Ocean Beach. This Muni train will take you all the way out to the ocean, and drop you off a block away from the Zoo. Be aware that there is a slight temperature change from downtown to the Sunset District, and a light coat is always a good idea.
***Baker Beach (on a sunny day) has amazing views of the Golden Gate Bridge and is a great place for a picnic. You will also see the Seacliff homes, many of which house celebrities like Robin Williams. Don't stray too far towards the bridge, however, or you'll end up with an eyeful of nude beach!
***The Japanese Tea Garden in Golden Gate Park is a great place to roam, and has plenty for children to be in awe of. This is also near the De Young Museum which has outstanding views of the city in its tall tower, and the Academy of Sciences. But, if you guys really aren't museum type people, the high prices of the museums will be a turn-off.
***In Golden Gate Park you can rent old time looking bicycle cars(4-6 seaters). These can be rented by the boathouse, where you can also rent peddle and paddle boats for hour usage.
***Catch a Giants game. You can ride the muni train just a short distance from the Powell Street Station and be dropped off right in front of the ballpark. There are a lot of kid activities, and the views of the bay are phenomenal. Plus, garlic fries and Gordon Biersch. mmm.
***If you have a pretty penny to spare, Teatro Zinzani is an unbelievably fun and interactive dinner show along the Pier's "F" Line, which highlights antique street cars.
If you want to see "real San Francisco" neighborhoods, I would recommend catching a cab or riding the bus to Noe Valley, Mission Dolores(beautiful and sunny park which hosts monthly movie nights), or the Marina/Cow Hollow district(which has numerous cafes and stores on Union Street).
In reality, San Francisco is a very small and friendly city. You will be able to accomplish a lot in just two days. Have fun, and don't be afraid of Muni, just be aware