If you go during the annual Barcroft open house weekend, you can drive all the way to the Mt. Barcroft Station. They have numerous lectures and displays of their work. It's well worth the extra effort to get there. But...I would recommend renting a 4-wheel drive vehicle in Bishop, instead of trashing your nice Accord.
We learned alot at last year's open house, including the amazing Blast Project.
The altitude at Barcroft Station is about 12,500. From the station you can hike to the summit of White Mountain Peak, which is just a little lower than the summit of Whitney. Check the following website for open house dates.
Here is the station's website:
http://www.wmrs.edu/
