score:4
I don't think you'll have problems entering the Yosemite Valley in April. The road you'd be taking would probably be CA State Rte 99, which is clear any season and is one of the major California routes. CA 41 and CA 49 will probably be clear up to the valley, but crossing the range might be problematic (CA 120). Haven't been to Sequoia yet, but its similar to Yosemite weather wise.
You probably won't be able to climb the Half-Dome, or go to the Glacier Point, but you will still see the marvelous Yosemite Valley and it will be in its best.
All the rest shouldn't be a problem any time of the year.
Upvote:1
If you do make it out to Las Vegas area I would recommend Red Rocks outside of the city it is worth the time. Beautiful area and you can drive thru it and also get out and stretch your legs thru part of it too. You can see some neat petroglyphs that aren't to far off the road. it you don't make it that far make sure to visit the Golden Gate Bridge in San Francisco by at least walking across it near sunset or sunrise it is a great site to see.
Upvote:1
To check if a particular California highway is closed due to seasonal weather, use the California Department of Transportation road conditions page.