Yes, when I think of "romantic getaway in Japan" Osaka and Nagoya are definitely NOT the cities that come to mind. That would be sort of like having a romantic getaway in downtown Cleveland.

An onsen resort in a pleasant mountain area would be great. There are plenty of options all over central Japan, although I don't have up-to-date info on any of them. You could get a traditional-style or Western-style room with a mountain view, meals included, and all the baths you can handle, perhaps even some quality time in a couples' bath.