As you may have guessed by now, Bruce, the only thing wrong with your plan is extending your trip by days, rather than years. There is so much nice scenery around where you'll be, you'll have trouble narrowing your choices. All of the suggestions already mentioned are excellent.
The key factor may be whether the Tioga Pass is open when you reach Yosemite. If so, I'd concur with the suggestions of heading over to Highway 395. From there, Mono Lake, Bodie, and various other great locations are within striking distance. And, as noted, be prepared for temperature extremes. Bodie, for example, is above 10,000 feet, and can be quite cool even on a nice June day. Sun screen is essential, too. If you do a search on Highway 395, you'll find a couple of good sidtes that can help in your planning. By June, Death Valley is a bit too toasty for most folks and most film - unless you have a good ice chest for the film.
Whatever you decide on, it should be a memorable trip, though. Have a great time.
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