I consider this trailhead and every inch of these trails as my home. I've run every single centimeter of the entire range.
1. If you want a casual hike/walk/view go from Lost Dog to Taliesin and enjoy yourself. Lots of kids, bikers, hikers, dogs etc. Some will even bring a picnic up to the lookout point at Taliesin. As a Trail Runner it's also extremely pleasant and graded gradually. There and back is just a tick over 4.3 miles.
2. If you want to be a little more aggressive try running out to Taliesin and then back but then go counter clockwise and run the old jeep trail to the joining point with the Ringtail trail. Take a right going back to the Lost Dog Trailhead for a total run of about 5.5miles. The joining point of O.J. and Ringtail gives you a very quick (and the last one of many) climb of about 200 feet up. I call it the Liberty Bell because I run at absolute full speed up this short but furious climb and "ring the bell" in my head. Quite Liberating.
3. And finally as an excellent run/hike go from Lost Dog straight up to Sunrise Peak. Fantastic climb to the Summit which has world class 360 degree views of all of Fountain Hills, including the fountain, the Superstition mountains, Four Peaks, Scottsdale, Camelback and Squaw Peak, all of the reservation, Thompson Peak.....just spectacular. Round trip up and down is around 6.4 miles.
4. It's extremely easy to add all these trails together as well. Up and down Sunrise with addition of OJ/Ringtail puts you at an even 10miles if that is something you're up for as well.
Enjoy my back yard!!