I guess the majority will probably say the Anju and Kafei side quest, don't get me wrong it's great and all, but it just drags on. The side quest feels like a chore, especially when you have to do it again. Also, the fact that the plot line is separated by lots of running around Termina, time travelling, being patient, it kind of takes away from the emotion you're meant to feel during those final hours as you're just glad it's over and done with. I will say this though, it's probably the most thought-out and intriguing side quest in the series.
My favourite would probably be the Gilded Sword side quest. You could argue that this is even more of a chore than the Anju and Kafei one, but the difference is, I actually enjoyed each sequence. First off, I love the Snowhead area - the music, the erry atmosphere when you first arrive, the residents etc. Secondly it contains one of my favourite mini-games in the series, the Goron Race. Also beating Goht again is always fun. The main difference between this side quest and Anju and Kafei side quest though, is that this one is actually worth it. You get a sword upgrade rather early on (probably the best design in the series), while the latter side quest offers little of worth especially since you'll complete near the game's end.