I'd have to agree with Plavt on the kimono thingy, not so much on the offesive part but you need to know your fiance would actually go for that and not feel odd as that's how it would kinda be. There's a lot of culture surrounding it that you'd need to bone upon before embarking on that, it would hard to arrange, and quite difficult unless you spoke Japanese well. And expensive.
The idea of Tokyo Tower was about the only thing I was going to suggest when I saw this last night. They also have a big ferris wheel just outside the city near Tokyo Disneyland. Pretty nice there.
Japan is probably more romatic to a foreinger than those living there, many of whom would probably go somewhere like Europe or Hawaii or Bali for someplace romantic.
The onsen/ryokan idea in a place like Hakone or Kyoto is not a bad choice, either, though a bit on the reserved side. Don't get me wrong, I love those places but would not be my first choice to propose.
Fuji is beautiful from afar, but pretty ugly up close, as in on the mountain.
A nice place, however, is lake Kawaguchiko, which looks out on Mt. Fuji
http://tamara1beth2eslinstructors.com/K ... 20Fuji.jpg
You won't get much snow for the traditional Fuji view this time of year though, but it's still beautiful. What you can get from around now until mid-August are the summer festivals like the hanabi matsuri in any town if you like a traditional setting and to view fireworks the Japanese way. Very nice. That's one of the few places I'd wear a yukata as a foreinger.
Kanegawa on the west coast is also nice.
Good luck and have fun.