time and distance I quoted is for the Lake George to Crest and back route. Crystal Lake would be shorter, Deer Lake would be longer. Whole circuit even longer - see below.
Mammoth Crest this link shows the whole route of the Mammoth Crest. On the trail profile shown, which I have done from right (Coldwater Cr/Duck Pass end) to Deer Lakes to the left (Lake George), is a long wonderful hike. The shorter acclimatization hike you want would be from left ( Lake George) toward the right. You can see that the junction to Crystal Lake is only 2 miles or so, one way. Turning left to the lake and downhill some, gets you to Crsytal Lake with views of the lake, Crystal Crag, and the Mammoth Crest. Turning right at the junction gets you near the top of the actual crest to an area of red volcanic scree, a very colorful scene. Once at the top, the views really open up. A morning start is best for coolness, and sun on the east facing Minarets rather than in your eyes.
Picture of Deer Lakes is in this link. You would not go this far.
Mammoth Lakes Trail System in that same link, there is a map without much labeling, but the trail starts on the left at unlabeled Lake George ( above labeled Lake Mary), then ascends to the junction and short spur trail turning left (actually you would go more or less straight) to unlabeled Crystal Lake, or at the junction turning right to unlabeled Mammoth Crest. I have had friends blow right by the junction and miss the turn somehow.
Mammoth Crest Trail map 
