Hi Yury, as you can see, no shortage of opinions on topics like this
There are many options near Mt Whitney to design an acclimatization approach which works for you and your particular schedule. As Kurt said, the rule is climb high, sleep low (meaning you want to expose your body to a higher elevation during the day than the elevation you sleep at, not that lower is better). You can get elevation by walking around at Horseshoe Meadows (10,000') or the Portal area (8500') and your sleeping elevation choices are Lone Pine (3700') or campgrounds between Lone Pine and the Portal (6,000'), the Portal, and Horseshoe Meadows. Ideally you would arrive in Lone Pine with enough time and daylight to drive up to one of the higher elevations and walk or hike around for an hour or two before descending to a lower elevation (perhaps Lone Pine) to sleep the first night. The next day, I would go higher (maybe hike from the Portal partway toward Lone Pine Lake or even to the wilderness boundary, which you can do with no permit for that day) and choose a higher sleeping elevation than the night before, but lower than you spent the day at, either a campground such as Lone Pine campground or the Portal. I agree with the other poster that sleeping the second night at the Portal confers an advantage in getting going in the morning, as well as acclimatization, but as Kurt points out, many people don't sleep well on the ground or in their car and would do better with the extra rest gained by sleeping in Lone Pine instead. You have to evaluate all these factors and then choose your strategy. After you have done this a few times, you will know what works best for you.
