My first hike at South Montains State Park, southwest of Hickory, NC. This is a big, remote park with all mountainous terrain. The hills are not terrible high (none over 3000 feet, as far as I could tell) but the trails have two orientations: up and down. Camping opportunities are abundant -- and 40 miles of trails deep into the backcountry of the park offer many backpacking options. Centerpiece of the park is High Shoals Falls, which is only a mile from the trailhead at the main parking area. Note it's a very steep climb in places, so it cannot really be called "easy" despite the short distance. Trip write-up at Two-Heel Drive.
Be careful around the waterfall, a misplaced slip could do you in. There's a great overlook at Chestnut Knob -- it's a steep climb to get up there but it's worth the effort.