Spending a day or two at Horseshoe Meadow is a great idea. Lots of nice day hikes. However, be careful of the free ranging cattle, including a bull.
All the campgrounds are 'walk-in', which means you will have to park in a parking lot and haul your gear to a campsite. Not a huge deal, if you will be using your backpacking gear. Could be a hassle if you are bringing the full on car camping gear with the huge tent and camp kitchen. There are bear lockers, but they are shared lockers. As I recall, 2 large bear locker between 3 or 4 campsites.
If you want to have a guaranteed spot, you might want to try to stay at one of the Whitney Portal sites. Reservations can be made for most of the sites.
