I would recommend camping at the Portal and taking a day hike up to the Lone Pine lake sign, which is around 10000 feet. It's 3 miles one way and it's just before the permit zone area.
I believe active acclimation, without overdoing it, is more effective than just hanging out. Of course you can always turn around early, before you get to the sign (heck, you can also head over to the lake by turning left at the sign, which is only about 5 more minutes away) if you don't want to exert yourself too much.
