It's good to hear you are planning on a couple of nights at HM as it will serve you well on Whitney. I understand your anxiety of not being able to get a site at HM (been there!) but you have to realize these are "walk in" sites that require one to transport there camping gear from the parking lot to their site so that pretty much eliminates the lazy types and the RV campers. Most of the campers I have talked to there are hikers and backpackers so you will amongst a friendly crowd for the most part.
Also, there's some easy hiking in the area that I would encourage you to take advantage of in order to help further acclimate. Last year I took a sandwich and some snacks, leisurely hiked about an hour, and ate by a stream and watched the trout dart around in the water. So relaxing!
