Yes, you should really come out. If Plan A doesn't work, there are plenty of options for Plan B. But you should expect to get a walk-in permit for Whitney.
Options for other places to see (and day hike):
Mt Langley (just S of Whitney)
White Mountain (NE of Whitney in the Inyo/White mountains)
Mt Dana in Yosemite starting from Tioga Pass
Clouds Rest in Yosemite, starting near Tenaya Lake.
Others can give you plenty more options.