Mt. Princeton is a fairly straightforward and unexciting mountain, as far as 14ers go. Following a treacherous drive up a dirt road (if you're confident enough to make the trip) it's just a short hike up some more road before turning up some singletrack and continuing on some talus to the ridge and summit.
As always, bring rain and sun protection. While this is a shorter hike, it's still a 14er. Even fast hikers should plan on 4 hrs round trip under perfect conditions. The north-facing ridge of this mountain holds snow late, sometimes until July, so be prepared for more hours on the mountain. 10 hrs isn't improbable for slower hikers.
From the center of Buena Vista, drive west on County Road 306. In 0.7 miles, turn south on CR 321 and drive 7 miles. Come to a fork and bear right onto CR 322. Drive under a mile to another fork, one for a ranch and one, clearly signed, for Mt. Princeton. Turn right for Mt. Princeton. Park here (8,900 ft) if you have a Subaru or less, or continue driving up the road if you're piloting something burlier. Over 3 miles up the road there are some radio towers with pullouts for 8 cars or so. There are a few campsites here as well, around 10,800 ft. Unless you're comfortable driving on a narrow shelf road with rock steps and bumps, park down low. There's nowhere to turn around for 3 miles.
From the upper TH at the radio towers, continue hiking up on CR 322A (the road away from, not toward, the radio towers). Continue for about 1.5 miles on the road before turning right onto Mt. Princeton Trail
at 11,800 ft, just a few minutes after breaking tree line. The Jeep Road continues up along 13er Tigger Peak and is accessible by car for 1-2 months of the year.
The beginning of this trail remains class 1 but is absurdly steep. The grade relents after about 200 vertical and the trail continues below the Tigger-Princeton ridge. It's class 2 from here on out. Talus hop cautiously before continuing up some switchbacks to reach the ridge at 13,100 ft. There's an old trail below the switchbacks, but it more or less dead-ends below the ridge.
Once on the ridge, don your wind protection and continue toward the summit. Cross along some flat areas by some rock features until you reach 13,500 ft, after which the grade cranks up. Continue up some excellent class 2 trail to reach the summit - it's just a short stretch from here.
While one would expect marmots and pika, I didn't see a single creature this entire hike.
Mt. Princeton, while first summited in 1877 by an alumna of its namesake, was named years prior by Harvard graduate - and Wyoming high point namesake - Henry Gannett.