There are routes in the east mountains but they may be longer than half day as they have limited access points as they go through long valleys.
From Niles Canyon, Palomares Road northward toward Castro Valley (Route 580). You can get back to the 680 and loop back to Fremont on superslab, or you can continue north on Redwood Road and then Pinehurst toward Orinda/Rt 24. You can use Rt 24 to get to 680 for a return trip (superslab) south past Walnut Creek, Danville, Pleasonton and back through Niles Canyon again. Technically, you can continue north on Grizzly Peak Blvd or get over to San Ramon Dam road. There is good riding in the valley between the east mountains and the central valley, just takes about an hour from San Jose to get to some 'jump-off' points.
If you are ambitious and want some great views/scenery.....go over Mt Hamilton (stop at the Lick Observatory), come down on the east side and take Mines Road back toward Livermore. Mount Hamilton is not a sweeper ride, more technical switchbacks, some narrow sections of road but the pavement is pretty good on the way up on the San Jose side of the mountain. This is a full day ride, takes 1.5 hours to go up Mt Hamilton, spend an hour at the Observatory (pretty cool tour there and scenic views), about 30-45 minutes to descend to Mines road, maybe an hour to get to Livermore.
In the East Foothills.....Niles Canyon (Rt 680) and take Calaveras Road back south, it hooks up with Felter Road and then Sierra Road back into San Jose. Calaveras can be a bit broken up, a mix of decent road with some goat trail like sections. On Sierra there are some hairpin tight turns on the way down into the valley that you got to watch (easier going down).
Nice views from all those foot hill roads.
There are a few loop east of Walnut Creek and San Ramon, you take the 680 north and then start on Boalinger Canyon and head north, a few different loops back to Walnut Creek.
If you only have a half day......most of those rides may be long, Calaveras Road may be your best choice as you can use a few ways to get into the valley.
Have lunch in Niles (there is a good pizza/burger joint there and other places) or Sunol (the café there makes really good burgers).
Honestly if you want a nice sweeper ride where you can do 50 mph the whole way, Uvas Canyon between San Jose and Morgan Hill is a nice ride, and then take the Santa Teresa/Hale back north (to stay off the 101) through the farms. Lunch in Morgan Hill is really good.
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