I started the Strawberry ride and managed it for 6 years before I got tired of putting it on and turned it over to Howard and Louise who have been operating it as AERC event. They still use most of the same trails I laid out back in 90s. I still enjoy riding this area and usually make a couple trips up each summer. There is a nice Cattle corral at Mill B that you can use IF the ranchers are not using it. They get first rights to it and if they ask you to move, You need to move your horses. And while strawberry is beautiful. It is not Wilderness.
I have also ridden in almost all of the North Slope trails. Blacks Fork, China Meadows, Henrys Fork, Hoop Lake, Spirit Lake. Beaver Dam Reservoir, and Brownie Lake. As well as most of the trails off the Mirror Lake hiway, East Fork of the Bear, Stillwater at Christmas Meadows, the Highline trail (into both Naturalist and Four Lakes basin), and around Whitney Reservoir. I've crossed over Rocky Sea and Cyclone Passes into the Upper Rock Creek area. But I've never rode up Rock Creek from below.
From the South Slope, I've gone in Grand Daddy Lake, Moon Lake ( both into Brown Duck Basin and Lake Creek) Up the Yellowstone River and into the Garfield Basin and Swift Creek in to the Timothys. South Slope is steeper, much more rocky, is a little more open with more Ponderosa pines around the trail heads, Usually starting at lower elevations, so more verticle climbs than trails off the North Slope. More Elk and fewer Moose.
I have not explored the WhiteRock or the Uinta Drainages. Something I guess I need to put on my bucket list.
Each of the areas have their own personality. The North Slope is more gradual in the climb, Dark forest of Lodge Pole Pines, lush meadows with lots of moose. You also usually start at higher elevation trail heads. China Meaodws and such are 9000 foot at the parking lots. Fish are a little smaller on the north slope.
Off the mirror lake hiway, you of course have way more people. The closer to Salt Lake you are the more used the trails become. Into Naturalist Basin is almost a hikers hiway, But it is a beautiful basin if you have never been in. Also the Forest Service requirement for the parking/use passes for any trail off the Mirror Lake hiway bug me. North and South slope don't cost anything to park and ride in.
Grand Daddy Lake like Red Castle both attract lots of scouts. So you will see several groups of them if you spend much time in the back country. I used to really like going into Kidney lake from Moon Lake trail head. But the Forest Service breached that lake and its just shallow reminder of what it used to be. It used to produce some Great fishing for 2-3 lb cutts. But I just don't know how the winters have been now that it's 20 feet shallower than the old days. But you can go past Kidney and into Squaw or East Basin. You will definitely get away from most of the crowds if you go that far.
Probably my favorite is from the Yellowstone Trail head and either going up into Garfield Basin or into the Timothy's. These are extremely rocky trails. But they seriously weed out the less dedicated back country campers. The Yellowstone trail follows the Yellowstone river and is a pretty gradual rise going up the drainage. When you climb up out of the Yellowstone Canyon, then you have some serious climbing into the Garfield basin. Swiftcreek on the hand going into the Timothys starts climbing as soon as you leave the trailhead. They breached the dam at East Timothy last summer, So I'm not sure what that has done to water levels in that basin. Famres lake is usually a sure bet to catch a few fish. And if you enjoy steep climbs, Bluebell Pass is nearby. Everybody needs to ride a horse over that pass at least once.
Cyclone Pass travels from Four Lakes Basin over into upper Rock Creek and passes over the Red ridge directly behind this horses left hip. I always end up tailing the horse up this climb. It's brutal.