That's a tall order, but there are still good options. Bianchi designed its new 24-speed Iseo ($549; bianchiusa.com) with a rider like you in mind. The hybrid Iseo, which comes in a men's and women's version, has a 700c wheel, which is ideal for pavement, but the Italian company combined that with lower gearing and an upright sitting position, which both allow for quality off-road riding. With a v-brake and mostly Shimano components, the Iseo is the ultimate bike to, say, tool around the Colorado College campus, then hit a dirt washboard Forest Service road on the way to Pikes Peak. If you want to use it off-road more than on, I'd recommend investing in a fatter, knobbier tire.
Out of Raleigh's "Performance Hybrid" collection, I like the powder-blue Alysa FT2 ($730; raleighusa.com). The bike has tough Shimano components, a lightweight aluminum frame, and 24 gears that will get you out of any gnarly singletrack jam. Plus, I'm a sucker for the soft blue frame and the aesthetic of the sloping top tube. Once again, if you plan to take this bike off-road often, invest in a beefier set of tires.