within San Francisco:
Noe Valley- both public and private schools in this neighborhood are great. Rents are high in this neighborhood. It is true currently the public schools are not based off an address and some schools (usually the desirable ones) are lottery based. Charter schools are also popular. Parents (and I am one of them) will drive all over the city if they can get their kid into the right school regardless of where they live.
If you would consider the peninsula (San Mateo County) look into the Millbrae, Burlingame, San Mateo, Belmont or Foster City School districts. Pacifica, which is on the coast, is also known for having good schools and also more affordable rents and is extremely family oriented.
For rents, check Craigslist for rates. You are probably looking at $2000-4200 for 2 beds depending on location and amenities (like parking).