Lee Vining may be the only reliable site for ice climbing on water-ice in California, though it is a long drive from Caltech (see map below). Some nice pictures of the walls and various routes are here.
Apparently there's a gas station with very good food here? I think it's closed in winter.
Lee Vining is located on U.S. Route 395 near Mono Lake. You drive a little ways along Tioga Pass road (rt 120). The pass is closed in winter, but you should still be able to drive far enough along the road to reach the turnoff (for Poole power plant). Please check the internet for latest parking restrictions; the power plant is private property, so follow all signs. From the power plant parking lot, hike west until you can go southwest up a broad gully, and then the ice will be obvious. Snowshoes or skis are sometimes useful for the approach. With firm snow, the approach should be about 30 minutes, but it can take up to an hour. Be careful: this gully can avalanche. Also beware of ice falling from the walls. <googlemap version="0.9" lat="37.947446" lon="-119.210587" type="terrain"> 37.944248, -119.215994 Park here (if road is plowed -- it's not always) 37.941947, -119.224212 The actual ice 37.931056, -119.164387 Turnoff from 120 37.950348, -119.113232 Turnoff from 395 </googlemap>
From Sierra Ice Climbing:
Lee Vining offers pretty good ice until April, with a large wall (~3 pitch), medium wall and small wall (you can top-rope it with a long rope -- there are a few bolts in places too), and a 45 min approach. To get there, take 395 past the Mammoth turnoff and past June Lake. Take 120 West towards Yosemite (the turnoff is before the town of Lee Vining). In the winter, the road is closed; just before the closure, there is a left turn. Take the left turn, and you immediately face a T-intersection. Go right, and drive a few miles. There is camping along here, though the campgrounds are closed in winater. Keep going as it turns to a dirt road, and drive to the end of the road at Poole Power Plant. Park in the turnoff before the parking lot. Walk through the parking lot to the West end, and hike West for 1/2 mile before taking a left turn into the obvious canyon.
This area is popular, and is a bit too crowded during weekends in prime season. You should be able to get condition updates from forums (e.g mountainproject, supertopo, summitpost).
See also the ice report from SMG.
We have more info on this wiki at Sierra Ice Climbing.