Not exactly sure what you mean when you say "family holiday feeling". There are LOTS of good family hotels. However, in summer, average prices for most of those are about $125-$150. "Family Holiday Feelings" cost a little extra money.
Since LA is so spread out, there is no single place that is close to EVERYTHING. Most people who come here tend to stay in Hollywood, Santa Monica, or Anaheim. In Hollywood, I recommend the Orchid Suites, Hollywood Celebrity Hotel, or Holiday Inn Walk of Fame, all near Hollywood and Highland. Another one is the Best Western Sunset Plaza. In Santa Monica, the Holiday Inn Santa Monica is close to the pier and reasonably priced. In Anaheim, I recommend the Howard Johnson (HoJo) Anaheim, and the Candy Cane Inn. There is also a nice place in Burbank called the Best Western Media Center, very close to Warner, NBC, and Universal Studios.