Check out the South Beach/Mission Bay neighborhood which is near the Caltrain station (4th & King Sts) and also AT&T Park (where the SF Giants play). There is also light rail along King St. and the Embarcadero that goes downtown and other places in the city (even out to the beach).
This area is a bit upscale and expensive. The area has been redeveloped in recent years and many of the buildings are relatively new.
South Beach / Mission Bay.
You might consider living on the peninsula (the area south of San Francisco) in one of the suburban towns along the Caltrain line (except near the airport because of the noise). Millbrae would be a good choice as there is a combined BART/Caltrain station there with plenty of parking. Rent will be a bit cheaper than living in SF.