High Sierra Topix

As everyone notes, the group size shuts you out of Sierran Wilderness areas. If you still want to hit the Sierra from the S. Bay Area, my suggestion would be non-wilderness areas in the N. Sierra. For example, the Grouse Ridge, I-80 corridor region has many nice hiking destinations that you can use to string together a 3 night 20 mile trip. The Lakes Basin area also offers some good possibilities.

Mosquito problems in the northernmost Sierra will depend a lot on the weather at the time you go out. If it is reasonably breezy and not really warm at night, it won't be that bad, whereas if it isn't very breezy and the nights are on the warm side, it will be miserable no matter where you are in the Sierra. I am a total mosquito magnet, as are the other members of my family, so I am pretty sensitive to this too.

You ought to do some homework on coping with mosquitoes and simply target a lower elevation area that has less mosquitoes. I backpack in mosquito season every summer and receive few bites because I give them little skin. Probably not practical for young scouts due to limited clothing issues but even outside of the worst periods, one may pass through areas with them. So read this thread with considerable info and links:

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There are certainly a lot of lower elevation trails in national forest areas at least 10 miles long and not in wilderness. The problem is they are likely to be somewhat boring usually down in forest. Folks on boards like this are not aware of most of them for that reason.