You can scramble up the ledge systems above the boulder problem that guards the approach to Beckey's and Cheetah. I prefer this approach to going up past Graying at the Routes as described in the Ruckman guide. This will take you up above the lower East Gate routes like Snowflakes and Speed of Life. From here you can choose your route up to Flakes. I recommend the 10d that starts with a leftward traverse and continues on to a cool slab arete. The bottom of Flakes is on a ramp which affords a good view of the route. You can't miss it.
If after that you are feeling frisky you have several good options. Wild Things is crazy. The flaring bomb-bay is wild indeed and the initial crack is good but steeeeep. Take tape.
Or, you can easily toprope the routes on the lower East Gate. These are generally fantastic. Speed of Life is nice to TR first as the finish approaches groundfall potential, although I never fell to test the possiblity (by the way, its one of the coolest granite routes ever). Graying at the Routes can be TR'd with a directional (black Metolius, I think) in the crack above its topout and the rope through the anchors above Speed of Life.
Good luck, have fun. The East Gate is home to some of the coolest routes in the Wasatch.
"The consciousness of self is the biggest hinderance in the execution of any physical activity" - Bruce Lee