Well after enjoying the main quest I have fun trying to collect everything else and just messing around in the memorable places while just enjoying the welly thought out music.
Exploring the Water Temple is always amusing, entertaining and fun. I love the Lake Hylia, the atmosphere of the Temple, I love fighting Dark Link and I love the tunes in the temple.
(It is possible that I enjoy watching the dawn of Lake Hylia even more than the Temple on the bottom of it, I am not sure. What I am sure of however is that Lake Hylia is wonderful in every game it is to be found!)
My favorite thing to do in OoT was explore and listen to the great music in the game. The temples were the most fun to explore, especially Forest Temple. My favorite music, besides the ocarina transportation songs, is the Forest Temple theme.
After beating the game, I like returning to the dungeons and just messing around there. I remember visiting the Fire Temple, and I found it neat using the Hover Boots past the lava in many rooms The Water Temple is also fun after you beat it, I think. And who doesn't like climbing Ganon's Tower and doing the final boss over and over again? I love doing that in Twilight Princess (off topic I know).
Just generally walking around, setting my own challenges for myself, speaking to people wearing different masks and the like to get funny dialogue, did you know if you already buy the zora tunic before unfreezing king zora he offers you a kiss instead?