Sorry to hear about your father's medical issues, that said, please tell him thank you for his service to our country. As far as your move is concerned, let me do my best to help guide you. Of course, affordability is relative, as the City is one of the most expensive in the country. That said, the further you're willing from the center of everything the more likely you are going to find an apartment that's friendlier to your pocketbook. Check out http://www.padmapper.com to see what neighborhoods will fit best with your budget.
Schools are an interesting conundrum here in San Francisco. Just because you live near a school doesn't necessarily mean that's where your child will be attending. I wish I had a better answer for you, but hopefully these links can help get you started:
To determine which neighborhoods you feel most safe in, I highly recommend a visit to: http://www.crimemapping.com/
Lastly, San Francisco has tons of nightlife of a variety of different flavors. Try a few places from this website to find your favorites:
Neighborhoods on the western side of the city like the Outer Richmond, Outer Sunset, and Parkside are often less expensive than other areas. The Excelsior and Outer Mission can be less expensive as well. If you're willing to live outside the city, you'll get more for your money in most areas to the east or south, and in that case I'd recommend checking out Alameda, Berkeley, Oakland, Daly City, or South SF. Generally speaking, it's said that the farther from the city you go, the cheaper prices get.
In addition to buyers and sellers, I work with renters to find homes that fit their needs. If you need assistance at all, let me know and I'll be happy to help in any way I can.
The more affordable areas seem to be the Excelsior in terms of single family homes as well as moving out towards the Outer Sunset as well (however, properties do not come on the market as often here). In terms of the school system here there is a lottery so it is irrelevant where you live. Your children could end up going to a school that is not in the district where you live. Here is a website with information pertaining to the San Francisco Unified School District and their strategic plan.
Thank you. Don't hesitate to contact me with further questions.