That is pretty early for the roads to be open. You should call the Inyo County Roads number just before your trip, and ask. 760-878-0202
I see you are flying into Las Vegas. Check driving times. I think you're in for lots of hours in the car for such a quick trip.
You might call the White Mountain Ranger Station in Bishop, and inquire about driving to Westgard Pass and up toward the Sierra Overlook (not sure that will be drivable in April, either, but it gets you high and is a great view of the sierra. Not much hiking, unless they open up the gate to the Bristlecone Pine forest. I think it's too early for that.
...or you might just stop and tour Death Valley. There are nice things to see there in April. It's 100 miles from there to Lone Pine.
