I'm not sure what your wife is so worried about - Tokyo is awesome - as is Japan in general. It's my favorite country to visit by far. Your biggest issue is going to be the language barrier. But nonetheless you can definitely do it and have an amazing time - just do yourself a favor and research as much as you can before you go. A GPS capable phone is also a great idea cause you will get lost. You can rent a local handheld or a mifi - but whatever you do avoid roaming on googlemaps or you'll owe hundreds in data roaming fees.
Also, though the exchange is pretty brutal, hotels prices have gone down due to the tourism downturn. I've found some great deals on Japanese sites like Rakuten and Jalan (need some Japanese or a lot of patience for the latter) that are generally better than what is offered on other web sites.
And IMO Tokyo and Japan in general have some of the highest PQR restaurant values in the world. If you don't need to blow out on high end sushi or kaiseki you can have great food at a reasonable cost. Hit the expensive places for lunch when they have much cheaper specials and go to izakayas or yakitori-yas or other less fancy places in the evening. Also, draft beer is good and generally pretty cheap compared to other big cities like NYC and London.
Long answer but seriously, you'd be crazy to have the opportunity and not go.