April is phenomenal in Utah. Go there.
(I do most of my hiking in either the Desert Southwest or the High Sierra. Unless you're a very experienced backcountry skier, the best parts of the Sierra will be inaccessible to you till sometime in June when the snow has melted. As for Hetch Hetchy, it is, IMO, one of the *least* scenic parts of the Sierra.)
In Utah, like most other places, many (most?) of the extraordinary hiking routes are not even in the national parks. Think of the whole place as a park.
If I had six days, I'd spend the first four backpacking either down Grand Gulch or down Buckskin Gulch/Paria Canyon. (Both popular trips, easily google-able.) Grand Gulch has the best Anasazi ruins in the SW; and Buckskin/Paria is probably the best slot-canyon hike in the SW. Pick your poison. Call ahead to find out conditions in Buckskin/Paria (sometimes there is too much water, or too little.)
On the remaining two days, I'd explore either the Needles area or the Escalante River drainage. Or perhaps spend two days in Zion NP, hiking the Narrows and Angels Landing.