Bears will break into vehicles with food, scraps, wrappers, etc. Even a cardboard box can invite the critters' attentions. So keep a clean car if parking there and use the bear boxes provided by the forest service.
The Whitney Portal store is a stroll away with famously good food, run by the same family since before I was a ranger there back in the 1990s. They have some last minute supplies too, if you discover you forgot anything from rain gear to a stove canister.
I'd camp here to hike Meysan Lakes and the start of the Whitney trail to Lone Pine Lake, neither of which require permits for day hikes. It's a great camp for acclimatization. The National Rec Trail gets overlooked, but showcases the transition from forest at the Portal to desert scrub at the bottom, following the stream, albeit from a neighboring ridge.
I'd also consider other campgrounds in the area, as there's a fair bit to do around Lone Pine for such a small town, and the Whitney Portal's position at the end of the road means you'll need to ascend/descend a mile in elevation over 13 steep and twisting curves every time you leave or return.
The bears and popularity of the Portal limit my enthusiasm for it a bit, but the positives of a store and restaurant, showers, and great hikes make camping here worth the effort for a few days. It's certainly a great way to get used to the thinner air if you're then headed for the back country.
If one had the luxury of time and the luck/good planning of getting reservations for Cottonwood as well as Whitney Portal, I'd check out both for additional hiking and fishing, as well as the Alabama Hills, which offer free boon docking.
The whole Owen's Valley is one great opportunity after another for all sorts of outdoor sports and enjoyment, but Lone Pine has more than its share of nearby attractions and the Whitney Portal is high on that list.