@maggiesch I don't think snow is a major worry this year in the Sierras...the SierraSnow Depth map shows nearly none. Last year there was no Sierra showing in June where this year it is all showing except for occasional patches.
The problem is more that parks are still restricted due to the pandemic. The places local to SanFrancisco...eg. Point Reyes, Big Basin, Mt Diablo etc generally require reservations that are usually in high demand and must be reserved 6 months in advance. However there may be some first come first served walking permits available once they open.
In prior years 40% of the wilderness permits for Yosemite were first come first served but this year they appear to have changed to a 14-9 day reservation system...hopefully temporarily.
Tahoe is the another "local" place and Desolation Wilderness is very popular...permits required but dispersed camping is generally allowed in National Forests with some restrictions.
National forest areas in the Sierras often don't require permits for overnight dispersed camping but you need to check with the local forest service.
There are of course lots of excellent hiking trails in the bay area.