> I feel like I've grown up oblivious to "my own American culture"
I don't blame you there, it's not exactly the richest of tapestries.
> How can I appreciate my 'own culture' more?
Look in to your own ethnic heritage, whether it's Saxon, Welsh, Gallic, Vandal, etc... there's a lot of deep history, culture and achievements there.
> "American culture", one of the most diverse and multi-culturally defined cultures in the industrialized world?
I'd say India is far more ethnically, religiously and culturally diverse than any western nation, whether we realize it or not.