Langley and White Mountain are both excellent alternatives, and they are good preparation hikes to see how you might feel hiking to Whitney's elevation. They are both easier than Whitney, since the Langley trail head is at 10k, and White's is 12k.
If you went to Lone Pine with the idea of hiking one of them as a plan, but dropped into the Visitor Center, you might be pleasantly surprised at the availability of a walk-in Whitney permit.
If you are in good physical condition, the biggest thing you need for preparation is a night or two at elevation before attempting to climb above 14k. If you give yourself enough acclimatization time, you will have a good climb -- no matter which peak you aim for.