As for the ride ....
We most often leave out of town by going out the back way towards sheep. The easiest way to find the trail is to go behind the super 8 and take a left. Head back towards the school and then take a right. The trail will switchback up the hill above cooke and open up on top of the ridge that has lots of play areas. If you stay left you'll end up over in sheep and if you follow the ridge/drainage on top or to the right you'll come out by daisy. Drop into daisy and crossover the large valley to wolverine or drop off daisy and hook right and head towards lulu. Either way you can loop around and work your way back to town coming in from the main trail east of town.
If you head out of town on the main trail as most due (be sure to go sloooow past the beacon check station as you leave town. The green light means your beacon is on and working and a red means its not) you can't miss the main trails to daisy or lulu and lots of riding in between.
If you do not mind a loooong trail ride to great snow and very scenic riding head out east of town past daisy, lulu, up and over the pass on the main road out of town to the top of the world (this is wyoming and you will need to get a wyoming license for $25 or if you get caught its a $100 per sled). You will go by a parking area (parking lot for guy's coming in from wyoming) and get on a trail system behind the parking lot and that will take you all the way back out to the main hwy. Ultimately you will end up on top of the beartooth pass if you go far enough with huge meadows, hills, lakes, views, etc... Takes all day with a gallon or two of extra fuel just to be safe but worth it if you have never made the trip before I think. Lots and lots of big open play areas once you get past the motel/store thats on top of the world.