For the Fussen area a car could be nice, but I wouldn't want to have one, myself, for Lucerne nor Murren.
For a place to stay in Murren I recommend www.eigerguesthouse.com.  They have some rooms that have extra beds, and are adjoining, if you have a larger family or simply need more room.  Nice game-room area if you are traveling with small children -- or just want to be able to 'take a vacation from your vacation'.  The restaurant onsite here is top notch -- so grab a meal here even if you don't stay here.  Stayed twice, 7 total days.  (30-somethings, toddler, friend, teen).
I've also stayed down the mountain in Interlaken, and up the mountain in Gimmelwald, if your city preference changes I can make recommendations in those two places as well.
I've stayed at a nice place in Fussen... but am drawing a blank... I'll try to come back if I think of it.
I wouldn't recommend where I stayed in Lucerne -- overpriced chain.
Near Fussen... go on a picnic by the lake, definitely do the luge, castles (of course).