What to do when there's no skiing
There is a trail listed on this site called "Up Dragons Back to Seven Lakes Point". This hike is listed on a Falcon Press Book that I don't own and on Trails.com, which I don't subscribe to. I don't know where Seven Lakes Point is since Mammoth Mountain Ski area doesn't mention it and it doesn't appear on any of my topo maps. I'm confident that Seven Lakes Point isn't all of the way up the trail, so this hike description is probably more complete than the Falcon Press/trails.com description.
The Mammoth Mountain Ski Area website lists the hike as a shuttle hike. That means that they expect hikers to park a car at Twin Lakes, take another car to the main lodge and buy a ride up to scenic gondola to the top of the mountain and hike down. There is a similar trip that people take during the winter which involves skiing the Hole in the Wall trail, which is out of bounds from the ski area. However, this is permitted if you clear it with the mountain and the forest service first.
You could do the shuttle hike if you want or you could park your car at Twin Lakes, hike up to the top and hike back down. Why not? It's double the fun after all. Actually, the trip up is fairly strenuous.
The lower part of the hike is through a mostly forested trail south of Dragon's Back, which is the ridgeline that marks the southeastern boundary of the Mammoth Mountain Ski Area. The trail passes a natural bridge that is called the "Bottomless Pit". During the ski season, the Bottomless Pit is called "Hole in the Wall". It is very steep, but it holds snow and is skiable.
After passing the Bottomless Pit the trail switches back and forth a couple more times along the southeastern side of Mammoth Mountain before reaching the Dragon's Back. Along the Dragon's Back you'll get glimpses of the ski area on the other side of the ridge. The Dragon's Back ski run is an expert run, so it is quite steep below the ridgeline. Along the Dragon's Back, particularly as you near the top of the mountain, there may be a lot of snow. In fact, if the Winter snowfall was heavy, you may not be able to make it all the way to the top until Summer. As of April 2, 2011 the mountain received over 600 inches of snow. After that much snow you likely won't be able to make it all the way to the top until July.
After a while the ridgeline opens up. You're nearing the top of the mountain now. At this point you should pay attention to any nearby mountain bikers. The trail crosses a mountain bike trail call "Skid Marks" and mountain bikers can travel quite fast through this area. At this point you are near the top of a ski run called "Dave's Run", named after the founder of Mammoth Mountain Ski Area, Dave McCoy.
At the top of Dave's Run the single track trail you've been hiking on ends and the remainder of the hike, a quarter mile or so, is along a dirt road until you reach the gondola building at the top of Mammoth Mountain. The actual top of the mountain is to the right of the trail just before you reach the gondola building. There is a benchmark there that tells you that the elevation is 11,053 feet. Enjoy the hike back down.
WARNING! Hiking and outdoor related sports can be dangerous. Be responsible and prepare for the trip. Study the area you are entering and plan accordingly. Dress for the current and unexpected weather changes. Take plenty of water. Never go alone. Make an itinerary with your plan(s), route(s), destination(s) and expected return time. Give your itinerary to trusted family and/or friends.