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In the years since my first visit I've returned to Tōdai-ji 東大寺 several times with friends and family, and it's always the hall itself that is most impressive to me. It's a wonder of wooden construction and deservedly a UNESCO World Heritage Site.
As is common with structures of ancient temples that are still present today, the building is not the original – it's been destroyed and rebuilt several times due to fires. So while Tōdai-ji 東大寺 was established in the early 8th century, the current hall is only 316 years old, and although it's difficult to imagine the engineering that must have been involved for such a massive design, the hall that preceded it was some 30% larger. There are detailed scale models of the current and previous halls inside, which are a great inclusion.
Nearby, one of giant supporting columns has a hole cut through it in the same dimensions as one of the statue's nostrils. If you're so inclined, or simply goaded into it by fellow visitors, you can try to squeeze yourself through it. If successful, it's said that you'll gain enlightenment in your next life, but either way you'll definitely get a good memory out of it!