Gerudo Valley
Times flows normally at Gerudo Valley, though there is no differences between its daytime and nighttime versions. There are two Pieces of Heart, four Gold Skulltula and one Gossip Stone to be found here.
When you first enter Gerudo Valley from Hyrule Field, you'll come to a wooden plank over a small pond; little of value is to be found here. Proceed and you'll come to a large bridge over a deep gorge (the bridge is broken in the future before getting the Gerudo Card), which has a strong river running through it. Adult Link can cross the bridge to the next point, but Young Link's route there is always blocked.
Adult Link can cross the gorge using Epona or the Longshot before the bridge is repaired. Once accross, he will find the Carpenters' Tent and the entrance to the Gerudo's Fortress.
Either Young or Adult Link can dive down the gorge and into the river. You can swim to the bank, on the same side of the gorge as the Gerudo's Fortress entrance. Young Link will find a Gerudo, cow and soft soil patch here, but there isn't much for Adult Link to find. If you plan on swimming along the river, be wary of Octoroks. You'll find yourself washing into Lake Hylia if you dive down the gorge.
Only Adult Link can participate in the Marathon, and he can only do so after obtaining the Gerudo Card. Enter the Carpenters' Tent, and the Marathon Runner will offer to challenge you to the Marathon. No matter what time you score he will always beat you by one second, but there are rumours that if you can get some kind of armour for Epona you can go fast enough to beat him. I can't confirm it, so whether or not you believe those rumours is up to you.
The Marathon route is from the Carpenters' Tent to The Lost Woods. You will have to actually enter the woods from Hyrule Field, then talk to the waiting Marathon Runner at the bridge. There is no real trick to getting the best times here, just choosing the shortest route and making a minimum of stops. If you're going to ride Epona for this, be careful about your route because if she gets spooked, it'll shave precious seconds off your time.