Three things come to mind. California is large- depends on which end of the state you will be in.
Lost Coast. Up north. 7-8-day trip if you do the whole thing from Matolle Beach to Hwy 1. I have done this twice and April is a perfect time. It does help to have low tides but not impossible even at high tide- just not as much leeway in getting over some points. You also need transportation from one end to the other - it is almost a 4-5 hour trip to get back to the beginning, not because it is that much distance but roads are bad and slow. There is a commercial shuttle service that works well, but is expensive. Lots of information on internet. Just "google" Lost Coast. No problem with permits either- you just self-register.
Grand Canyon - good time of year for this. There are some longer trips. One problem is getting a permit. From Southern California (LA area) it is actually closer to the Grand Canyon than northern California. Zion National Park in Utah is another option.
This year looks like a normal to higher than normal snowpack in the mountains. April in the Sierra is going to be a snow trip. Early April is also quite different from late April.
This probably would not appeal to you, but April is the time PCT hikers start from the Mexican border. There are plenty of 10+ day trips on the PCT before you even get to the Sierra! They are plenty remote- but not what you likely had in mind.