4.7 miles, 1-3 hours
This hike is about 4.5 mile round trip and can be done easily in less than 1.5 hours. It starts at around 800 ft and drops to 600 in .25 mile.
Then it meanders till the start of South Rim Trail. There it climbs about 300 ft in 0.3 miles. There is a nice bench there if you are inclined to stop. Keep going to keep the cardio up.
The next 0.8 miles climbs another 250 ft to 1150 ft elevation. Some incredible views can be found here overlooking the valley below and Silicon Valley in the distance. There is an optional steep switchback located here. Drops 850 ft in 0.9 miles.
It's downhill after this. Go 0.4 miles. Another beautiful view with a bench giving an amazing... and I mean amazing view of the bay framed by the east bay hills and the valley of Alum Rock.
From here it is switchbacks. About 0.8 miles, 9 or 10 switches and 500 ft lower and you come to where Penitencia creek & Arroyo Aguague meet at a set of benches and a beautiful stone bridge.
Its a wide road from here with Penitencia Creek to your left. If you look to your left (before getting to the main Alum Rock parking area) you will see the trail head for the steep 0.9 mile switchbacks I referred to earlier.
As you approach the gazebo, follow the road to up and to your left. This will take you back to connect up with Pigeon Creek Trail. As you reach the short trail to Inspiration Point (at the first hard bend to the left) you can grab the Pigeon Creek Trail (a small trail just to your left off the road after the left curve) back up to your car.
From 680 in San Jose, CA take McKee Rd or Alum Rock Ave east and follow signs to Crothers Road. Pigeon Gap road is on the left on Crothers. Park by the mailboxes. Trailhead is next to apartments. Don't worry its all nature after that.