Badly need advice. 5-7 days. California. Early April.

Yosemite is impossibly busy later in the season.  This might be a good time.

I’ve not been able to get into Yosemite valley but that has to be the most iconic place to go.

April in the Valley is a very good time  to go: few people; weather is warming and the  falls are beginning to flow. Higher elevations are accessible. Snow is compacted and easy to walk on; there’s so much granite that melts off that snow isn’t an issue for much of the time. And anyway the Valley itself is stunning and worth days exploring. And yes in March you can find solitude.

Sounds like you want to section hike a relatively snow free portion of the PCT and not travel that far from the Bay Area which are conflicting goals I think.

There have been other threads here on BPL about places and routes south of the central sierras. So perhaps start a new thread asking a more specific question about a desired location and or hiking conditions.