While I never want to actually replace my parents, who are pretty freakin' awesome, I would probably choose Gene Kelly for my dad. I'd hopefully inherit his wonderful dancing ability and I might have been able to hang out on movie sets with him and all the other stars of the musical era. Of course, if I was actually his daughter, I most likely wouldn't appreciate him or the lifestyle. That's how things go.
For a mom, maybe Jane Austen? It would mean a happier ending for her own love story and living in the Regency era, though I doubt things were quite as romantic as I imagine them to be. I can totally rock an empire waist, though, and I bet she'd have made a very 'cool' mum for the age she lived in.
Um, these are seperate fantasties, of course. Although, Jane Austen time travelling and falling in love with Gene Kelly would be the most cracked out historical fanfiction ever.