After a cross country flight I think that trying to sleep at Horseshoe Meadow at 10000 feet would mean very little sleep. You want to get a good night's sleep the second night before the hike.
What I've done to compromise, is to hang at Horseshoe Meadow as long as I can, then drive down to Lone Pine to sleep in the hotel you reserved. But now I stay at a Mammoth area hotel or condo, about 8500 feet, to take advantage of a nice bed while being at altitude. Kill two birds with one stone. Then I drive into Lone Pine in the morning, pick up the permit, shop in town for a bit, then head up to my campsite at the Portal.
I think the Portal area campgrounds at 8000 or 8400 feet are plenty high enough and you'll have a better chance of sleeping at that altitude.