You say you're new to SoUt, and based on the tenor of your questions I'm going to assume that you're not all that familiar with the peculiarities of desert travel (water finding and off trial navigation). With that in mind:
The needles district of Canyonlands NP has some great backpacking. Not very convenient if you're flying into Vegas, though.
3 days could easily be spent exploring Coyote Gulch in the Escalante. Another Escalante trip would be a loop through Silver Falls and Choprock canyons. A third Esc. 2-3 day loop would be starting at the Egypt trailhead, hiking down to Fence Canyon, down the river to 25 Mile wash (check out Neon and Ringtail canyons along the way), then up 25 a ways and back out to the car. This last option is the most varied and difficult of the three, and would be my choice.
Doing an overnight down the Narrows is a great trip, though mid-April creates a high likelihood of too much water (and cold water).
Going to Bryce Canyon and hiking some or most of the Below-the-rim trail would be very nice that time of year.
I could go on and on. Mid-April is a great time to visit that area, and the possibilities and endless. After you go, expect to want to return soon.