The few snow level stations are on the west side of Whitney. Here's a good CDEC page.
...Or the CWD (Cottonwood Lakes) station just south of Whitney.

If you go early in May, even if the lottery shows full, (because many people select May 1 just because it's the earliest in the year -- but they never show up!) you can walk in and pick up a no-show permit. Just look at the Unused Permits numbers, and forget paying the $$ for the lottery. Walk-ins are free.