Although experienced hikers will probably want to tackle Yale's east ridge, it can be hard to resist Princeton's dominating peaks from down below. If you have a 4WD vehicle, figure on 6.5 miles of hiking and 3200ft of elevation gain; if not, it's a grueling 13 miles and 5400ft of elevation gain. Either way, count on a long day.
The road itself is often harder to find than the trail. From the center of town, drive west on County Rd 306 for 0.7 miles. Turn left on County Rd 321 and continue south for 7.2 miles. Turn right onto County Rd 322 at a large sign. Drive 0.8 miles to a fork in the road; bear right and you'll be on Mt Princeton Rd.
If you have a two-wheel drive vehicle you'll be leaving it here at the large parking area (8900ft), and starting your walk up the road. If you have a high-clearance 4WD, you can continue up the narrow road. Bear right at the fork, and drive 3 miles to the radio towers (10,800ft). There is parking here for a couple of vehicles; or you can left and continue on the 322A Rd. Between 3.2 and 3.4 miles up the Princeton Rd, there are some small camping spots near 11,000ft, with some parking. After hiking about a half-mile, the road curves up to the left and heads south to the Lucky Mine. The Mt Princeton Trail will be on the right; follow it all the way to the summit. Remember that storms in the Collegiates can blow in fast, so don't hesitate to turn back if the weather gets dicey.