April will be cold in the northern part of Utah. My assumption is you'll be in the south eastern corner. In the southeastern corner April is a transition month. Spring will have sprung, but it could be cold or maybe not.
For things to see consider:
1. 4 corners
2. Monument Valley (I have always liked the Utah side of this valley)
3. Valley of the Gods (4X4 may be required)
4. Goosenecks State Park (on the back way to Valley of the Gods route 261 to 316). Drive to the end of the entrance road for a view you will never forget.
5. Mexican Hat, the town. Nice place to have lunch.65. Hovenweep NM
7. Canyonlands NP
8. Arches NP