To see most of the park in a single, moderately strenuous morning, take the Condor Gulch Trail from the visitor center. As you climb out of the parking area, the Pinnacles' wind-sculpted spires seem to grow taller. In less than 2 miles, you're among them, and Condor Gulch intersects with the High Peaks Trail. The view from the top spans miles: the Salinas Valley to your west, the Pinnacles below, and miles of coast to the east. And it's the most likely place to spot the elusive California condor. (Look for the white-triangle markings on the undersides of their wings.) After traversing the high peaks (including stretches of footholds carved in steep rock faces) for about a mile, the trail drops back toward the visitor center via a valley filled with eerie-looking hoodoos.
In another 1.5 miles, you'll reach the reservoir marking the top of Bear Gulch Cave, which closes occasionally; in 1998, it closed due to storm damage and to accommodate migrating Townsend bats, who in the past several years have come here to have their babies. It's usually open, but if you want to explore, you'll need your flashlight and you might get wet; still, this half-mile-long talus cave is a thrill. From the end of the cave, you're just a short walk (through the most popular climbing area of the park) away from the visitor center. It's also possible to hike just Bear Gulch and the cave, and then return via the Moses Spring Trail. It's about 2 miles round-trip, but you'll miss the view from the top.
If you're coming from the West Entrance, the Juniper Canyon Trail is a short (1.25 miles), but very steep, blast to the top of the high peaks. You'll definitely earn the view. Otherwise, try the short Balconies Trail to the monument's other talus cave, Balconies Cave. Flashlights are required here too.