There is a tremendous quantity of beginner backpacking destinations in the National Parks of California. There are some problems, though, for this year.
The snowpack in the Sierra Nevada range is extensive this year, and it won't be melting off early. There will be places up high where the snow will last until August. As a result, lots of high trails that would normally open up are not going to be available to you. This will force you into the trails at lower elevations. That's OK. Once you decide which park you are going after, you should be able to contact the wilderness permit-issuing office for advice.
Be prepared to compete with many other backpackers who are looking similarly. For example, many people show up at a permit office in Yosemite, and they say they want to go on a backpacking trail to a lake, no more than 6 miles each way, and no more than 1000 feet of elevation gain. That's fine, but that means that you will be sharing that lake with fifty others. If you go ultralight, your light load should allow you to go farther than the average backpacker. If you tell the permit office about 10 miles and 2000 feet, it will get you out of the range of the masses. Once you get out about 15 miles in a day, you will have the whole place to yourself, and then you can have a true wilderness experience.
I led many group trips to the Old Secret Lake, and the New Secret Lake, and we would seldom see anybody else. What was the trick? There are no trails going there. We had to navigate through the woods.