Could it be that the family wants to keep its address out of the paper? Or the paper itself has a policy of not publishing them? I know many small- to medium-town papers used to routinely include the street address of the deceased in obits, and even the addresses of siblings or grown children if they lived in town. Many of them abandoned that practice because burglars would watch the obits and go rob the home when they knew the occupants would be at the funeral.
In my experience flowers *always* go to the funeral home. Sympathy cards are mailed to the home of the closest survivor, or in some cases, to the survivor the sender was closest to (Example of the latter: If my friend Martha's dad dies, but I never met him or his wife, I'd send the card to Martha, not to her mom.)
It's also my experience that most senders of sympathy cards know, or can easily get, the necessary mailing address. If not, I suppose it would be OK to send cards to "The family of John Doe, in care of Smith Funeral Home." But the general rule around here is, flowers to the funeral home, cards to the family's home, memorial charitable donations directly to the charity (which keeps track and informs the family).
I've never heard of *bringing* a sympathy card to the funeral home. Mass cards, perhaps, but those are actually a gift. A plain old sympathy card isn't necessary if you are delivering your condolences in person.