Fortunately, though, you're on the right track. A "road" bike, with skinny tires and drop handlebars, would be uncomfortable and unsteady on gravel and dirtnarrow tires simply don't like loose surfaces. And a mountain bike, with its big knobby tires and (common these days) front AND rear suspension, is heavy, complicated, and way more than you need.
The solution? As you note, the hybrid or "cross" bike, basically a de-tuned mountain bike. These offer good performance on gravel or dirt roads, have plenty of gears to take the strain out of hills, yet also roll nicely on pavement.
There are lots of choices out there, as this type of bike has become popular in recent years. Most will set you back between $300 to $600. They typically have an aluminum frame, although a steel one will offer a superior ride, and also 24 or 27 speeds. More speeds doesn't mean a wider range (i.e., a lower or higher gear), but it will cut down the "jump" between one gear and the next for smoother shifting and an easier time finding the "right" gear. The main components almost always are made by Shimano, which is fine. Some also have SRAM shifters, fine as well.
A terrific example of this kind of bike is the Bianchi Boardwalk ($520; www.bianchiusa.com). It's a comfortable, well-designed bike, with a good component setup and a light frame (aluminum, but as I say, this is most common). Fine for pavement, gravel, even decent trails. A slightly spiffier bike is the Trek 7500, which sells for about $750 (www.trekbikes.com). Mainly, that's because it has both a suspended seat post and front fork suspension. Neither of the above is a real heavy-duty "trail" model, but they'll take some of the bumps out of the road. Spiffier still is the Marin Point Reyes ($1,000; www.marinbikes.com), which puts pretty high-end components onto a well-made frame. Really, an extremely nice bike, and the one you perhaps ought to buy if the birthday gift is that belated.