Former No Cal girl here. That's a LONG day (Yosemite plus other activities) but it could work. 17 mile Drive really is just a gorgeous drive through millionaire's row, basically, def. worth doing. You might do the Aquarium, then dinner in Monterey, then the drive BUT the scenery on the way to Big Sur is incredible...
Do NOT miss Pfieffer State Beach (natural bridges, windy rocky scenery, nice sand), Andrew Molera State Park is also a great short hike (meadow, butterfly grove, beach and bluff) and NEPENTHE even just for coffee.