Morro Bay is as good a choice as any. Plan on the drive down Hwy 1 from SF to Morro Bay taking at least 6 hours without stops.
If you think you'll need to stop sooner, then San Simeon or Cambria are good choices.
If you want to go a little further then San Luis Obispo or Pismo Beach would be your options.
While I'm not too familiar with accommodations in Morro Bay, I can recommend choices in San Simeon, Cambria, San Luis Obispo & Pismo Beach.
San Simeon: Best Western Cavalier (waterfront hotel with wonderful views) or the Sands Hotel (located next door to the Cavalier, but more affordable). Beach access is a stone's throw away.
Cambria: The Cambria Pines Lodge offers suites suitable for families. It's located in a forested area in town and has a restaurant on-site. They usually have a mid-week winter rate that may appeal to you. The Best Western Fireside Inn on Moonstone Beach Drive offers good size rooms and the ocean sits across the street with a lovely boardwalk for an early morning walk for yourself and your kids to stretch the legs.
San Luis Obispo: Embassy Suites, Sands Suites & Motel, Peach Tree Inn, newly opened Radisson or the funky Madonna Inn.
Pismo Beach: Pismo Lighthouse Suites (large room includes 2 bathrooms), Cottage Inn, Best Western Shelter Cove Lodge, Sea Crest Resort, The Cliffs Hotel, Mission Inn.