I have speed hiked the JMT NOBO 3 times leaving the car at the Whitney portal (twice) or in Lone Pine. There are two safe places in/near town - the Museum and the lot near the golf course - but you will have to pay. This strategy worked pretty well since hitching was easy (I also shared the ride with friends from the Valley to Mammoth on one of these trips) and there was no concern about theft. That being said, this year drivers may be more reluctant to pick up hitch hikers due to COVID concerns. Parking at Mammoth is not a bad option, but you will still need a ride back. Another alternative is to arrange a private shuttle ride - check out the Facebook JMT group for information. In any case, I would never long term park in the Valley - heard so many horror stories about break ins and stolen gear.
