This is not really an off the beaten path tip, it is just a tip about really taking the time to feel the beauty and awe of being surrounded by the gorgeous, giant trees. I had never seen anything like these trees before, it's truly awe-inspiring. While you are there, just soak in the scenery and get your picture taken hugging one of the lovable giants.
We were lucky enough to see this duo make their way from the parking lot at the Giant Forest Museum to the Big Trees Trail and then we watched them munch their way through the Round Meadow. We kept to the footpaths and the bears stayed in the meadow. We probably saw them on and off for about a half hour--it was pretty cool.
Not much of a contest--although this fallen sequoia is just a tadpole as compared to some of the true giants like the General Sherman tree which has a circumference of 102 feet. And if my geometry calculations hold true--that means its diameter is about 30 feet. This trees diameter can't be more than fifteen feet, meaning its cubic volume is maybe a fifth or less than the really big trees. End of geometry lesson.
If you drive up the mountain to hike the Moro Rock Trail, take some time to also see Crescent Meadow. It is an uncrowded corner of the park. There are no spectacular sequoias, but this meadow was one of John Muir's favorites. A good spot for quiet contemplation.
Keep your eyes open, the Sierra is definitely bear country. Bears are always a thrill and mostly they will ignore you. However, it is always important to keep your wits about you when you see a bear. For example, if the bear seems small in size, it might be a cub and you might have inadvertently gotten between the cub and its mother. That could be dangerous. Please do not attempt to approach the bears--they should not get acclimated to people. It is dangerous to the people and it is dangerous to the bear.
Sequoia, but even more King's Canyon, have an enormous backland. Only a fraction is opened with roads for the average family with cars. It must however be endlessly wonderful to backpack into the rough mountainland in and around the National Parks, something that I have high on my "wish-to-do"-list (including the same actions in Yosemite).
When you pick up your park information from the Ranger, pick any trail and it will povide you with an experience "off the beaten path."