I stay off site more than I stay on site - but when I do stay on site the trip is so much more fun. Off site, you only feel that you're at Disney when you go to the parks or to Downtown Disney. On site, you feel that you're on Disney 24/7.
I only feel it's a true Disney trip when I'm staying on property. The decor, restaurants, transportation are all Disney related. The whole trip overall is more magical. Not to mention the free transportation, dining plans, free dining, Magical Express, 4/3 deal and everything else that has already been said. Just have your wife come on here & read the responses you've gotten. That might help persuade her.
No matter what you end up doing - it's still Disney and you'll have a great time!