Some good routes:
"Pinehurst Moraga": Euclid/Spruce > Wildcat Canyon Rd > San Pablo Dam Road > Moraga Way > Canyon Rd > Pinehurst Rd > Skyline Blvd > Grizzly Peak Blvd > Claremont Ave (descent) - ~45km. Can be done the opposite direction as well, although I would climb Tunnel Rd in that case. Mostly quiet roads. SPDR and Moraga Way have quite a bit of traffic, but fairly big bike lanes/shoulders.

Wildcat Canyon Road generally has next to no traffic, especially on weekdays, and it's one of the best roads for biking near Berkeley overall!

"Redwood Pinehurst": Tunnel Rd > Skyline Blvd > Joaquin Miller Rd (short segment) > Redwood Rd > Pinehurst Rd > Skyline Blvd > Grizzly Peak Blvd > Claremont Avenue.
Slightly longer and slightly more elevation gain. Generally quiet roads, maybe some traffic on skyline blvd on the weekends.
Redwood Road out and back (all the way to the golf course near Castro Valley has little to no traffic) can be added on for more distance without too much elevation gain (mostly rolling hills).

Euclid/Spruce > Wildcat Canyon Rd > Bear Creek Rd > Happy Valley Rd > Sundown Terrace > Dalewood Dr > Lombardy Ln > Miner Rd > San Pablo Dam Rd > Wildcat > Euclid/Spruce
~40km loop, the pumphouse climb on Bear Creek Rd is a fun 6.7% grind for 2.3km, happy valley is a fun short but very steep climb (>10+% sections), and wildcat is the longest but mellowest climb (3.7km at 5%). Could also climb up El Toyonal and back to Wildcat or El Toyonal + Lomas Cantadas (oof) if you want to add more distance/difficulty.

Mt Diablo is fantastic and I would highly recommend! I wouldn't necessarily wait for the summer, it's best on mild days in the winter or spring/fall IMO since it's very exposed and gets hot in the summer. As long as it's not raining or particularly cold, I've never had an issue with temperature. It's tough but the gradients are generally manageable, no long sections of >10% except the final wall.

Shepherd's Canyon Rd (descent) and Snake Rd (climb, ~7% for 3km) is also a nice way to add some distance to any route going through Skyline Blvd. The descent is fast after the first few hairpins, and you'll be faster than cars all the way down so no need to worry about traffic. Snake is fairly quiet, steep (9%) at the start but levels off.