If your wife considers a dirt road, off roading, (which is the drift I'm getting) then I agree with a couple mentioned and that's probably the best toe in the water approach. FR 300 is doable by a car, with great views that are sure to hook. Mt Ord service road is doable by a car and has remarkable views and a touch of a "narrow" road for a noobie and a nice hike at the top if desired. The Apache trail is doable by a car and is just a must at some point if you live here, at least fish creek hill and hike to the cave or down to the creek.
Horseshoe Lake is also do-able by car. 4peaks as well but it's a zoo, I avoid that whole area. Backway to Mt. Lemmon would be nice for a future option once the hook is set, as it's just longish.
Maybe if it's "car-able," then that is a good, easy, simple introduction to "off roading" if I'm understanding what you're aiming for.