According to Google maps, the best route is through Page AZ and then Kanab UT on Hwy 89 then the last stretch to Zion's on Hwy 9. I've never been over the Hwy 9 route but also plan to travel that direction in May as well.
The alternative is a very long trip by way of Lake Mead near Las Vegas. If someone has a different route, I'd love to hear about it also.
Here's a link to the
map route.