Porcupine Flat or Tuolumne Meadows Campgrounds are closest to the trailhead at the southwest end of Tenaya Lake
I recommend Tuolumne Meadows Campground as it is higher and you'll get acclimated better, and you can make a reservaion there (Porcupine Flat CG is first-come, first-served only).
For availability of campgounds, see the unoffiical, but informative website
This site shows how many campsite reservations are still available for a given date--very useful. Reserve at the government website http://www.recreation.gov
You don't need a wilderness permit if you're out for just the day (that is, not camping overnight along the trail).