I agree with nishimark.

If these people were not the owners of an inn but friends of yours (perhaps Japanese people you had somehow met before coming to Japan), then a card and gift would be appropriate. It's fair to say that if you were staying in their home, in their spare room, and you weren't paying them, a gift would be mandatory.

But this is a business transaction, no matter how much the owners are putting themselves out for you. What they are doing may be some sort of standard New Year's package that they put together for all guests, not a special favor for you.

I would therefore not bother with a New Year's card, and while there is such a thing as New Year's gift giving, it isn't like Western Christmas gift giving. The children in a family receive money from their parents, relatives, and perhaps visitors, but adults normally exchange gifts only with people they have a business relationship with or with someone they owe a favor to.

For example, I once spent New Year's with a family, and the husband and wife gave a present to the man who had introduced them (someone they owed a favor to), to the husband's immediate supervisor, and to the wife's koto teacher. The only other gifts in evidence were envelopes of money for their two elementary school-aged children. (I brought some money for them, too.)

You know those legendary super-expensive pieces of fruit that all the "gee whiz" documentaries show? They're for giving to business associates, not for snacking on at home. The gifts given at New Year's tend to be rather impersonal like that.

Thank the owners profusely when you leave. Perhaps take pictures of them and their property and send some prints to them when you get home.

Definitely don't give them a homemade card. That would just be odd in a Japanese business-customer relationship.