Monterey and Yosemite on Fri-Sun during summer? Yikes, going to be busy. You'll be fine, deep breaths and accept that traffic and parking and crowds will be a thing. You do need to get accomodations sorted ASAP.
Campgrounds and lodges in Yosemite likely booked up months ago, though still worth a try. There are options if you're willing to stay outside the park and drive in.
I live in Santa Cruz on the north end of the Monterey Bay. I don't care for 17-mile drive, think it's overrated. Though maybe it's one of those things everyone should see once. Since you're bringing bikes the best way to explore Monterey is via the Monterey Bay Coastal Trail. Leave your car at the hotel, or park outside the city, such as Roberts Lake Park, and bike the paved multi-use path that goes right along the coast and avoid the traffic and parking hassle. The path takes you past the wharf, cannery row, all the way to Lover's Point in Pacific Grove. Then continue on to Ocean View Blvd and Sunset Dr before picking up 17-Mile Dr.
If the coast is socked in with fog (can happen during the summer months), you can usually go inland a few miles to find sun and warmth. Carmel Valley is beautiful, and has good wine tasting if you're into that sort of thing. If you don't want to worry about who's the DD then you can get a Lyft/Uber, though this will (if I remember correctly) run about $30 each way, which is still cheaper than a DUI!
Big Sur is awesome, but may be difficult to get a campsite/room at this point. Don't expect to roll in without a reservation and find a place to stay. There will be hoards of people and relatively few options. Parking for iconic places such as McWay Falls fills up quickly during the day, even mid-week in summer. The key is to get to see places very early, then do a lesser known hike or attraction later in the day.
Going straight from Big Sur to San Diego seems somewhat odd to me, skips over many great areas: Cayucos/Morro Bay, San Luis Obispo, wine country around Buellton/Solvang (who doesn't like going around quoting Sideways?), and Santa Barbara. It's your trip though, you do you.
Finally, Yosemite. If you can't find a campsite in the park, you may find something in the surrounding National Forests. These also fill up months in advance, so reserve ASAP. If you can't find a campsite within reasonable distance, there's also the option to disperse camp (boondocking, no facilities, not even water). Generally cannot do this on the eastern slope of the Sierras. There are places south of Mono Lake and in the Bodie Hills where it's allowed. Call the local USFS office for details.
The drive from Lee Vining to Yosemite Valley is rather long and the valley will be hot and super crowded. For these reasons I prefer Tuolumne Meadows and the surrounding high country during the peak summer season.
Lots of wonderful day hikes up and down the Eastern Sierras, too many to list.
On your way back to Reno, it's worth making a short excursion off hwy 395 to see Bodie State Park.
