Be aware that Sycamore/Hammon Grove are just above sea level, so temps might be high. GV is supposed to be 92F on Saturday. The lower Yuba River is worth visiting down there, though. Wet wading for trout can be fun!
If you drive farther up Hwy 20 past Grass Valley/Nevada City there's the Tahoe National Forest with quite a few dispersed camping options. Scotts Flat Reservoir CG is very close, but it's the Labor Day holiday, so check reservations.
Another area to consider is 20 miles farther up Hwy 20, turn left on NFS-18 to access Fuller Lake (day use), Rucker Lake, and Blue Lake. We often see people camping at several log decks (39.35992, -120.64207) on the rough road to Blue Lake. Blue Lake lives up to it's name and is a very nice swim, but is also popular with SUP folks. Cell service too. Farther out NFS-18 is Lindsay Lake, with nearby dispersed camping. There's good hiking off Blue, Lindsay and Carr-Feely lakes, if you have the time.
Almost to the 20/80 intersection is reserved camping at Lake Spaulding, and Meadow Lake just south of 80/20 is another option. We like to paddle Meadow Lake. It's approximately 45 mins from our Nevada City home.
Feel free to DM me for specifics.