GandC, my family and I have made a habit of spending 5 nights in Mammoth (8K') before heading to Whitney, usually doing some higher dayhikes in the area between 11K' and 13K'. It's worked great for us. If you really wanted to see how you're handling the elevation before hitting Whitney, I would suggest running up to the east entrance of Yosemite and hiking Mt. Dana. I believe this is the easiest, quickest way to get to 13K' in the eastern Sierra. It's a relatively short hike - maybe 4 miles each way - with about 3K' of gain, and you don't even have to enter the park (and pay the fee) to access it. The trailhead is just behind the eastern entrance station and there's plenty of roadside parking just outside the park entrance.
