Roads into the Bishop Creek drainage are all open - those roads are either State or County roads. Lots of folks are hiking on all forks of Bishop Creek, including overnighters. There are still a lot of backpackers doing the South Lake - North Lake loop hike, among other similar hikes. Federally run campgrounds are closed, but non fed campgrounds are still open. Big Pine Creek is open. Even heard of the Palisade Glacier?
There are literally dozens of big peaks to climb north of Mt. Whitney, with open access to trailheads. The only difference between Mt. Whitney and other areas is that you won't find a nicely maintained trail to the other summits. If you have never been in this area, give it a try, you won't regret it. Branch out!
You will not encounter Forest Service or Park rangers, but SAR services will still operate, since they are run by Inyo and Mono Counties, not the feds. Forest Service permit counters are closed, of course, but don't let that stop you.
http://www.sierrawave.net/26726/government-shutdown-impacts/
