Monday is a good day as many people are leaving after the weekend. Get there in the morning (9am-noon) if you can. No guarantees though--August is a popular month.
Of the list of campgrounds, the ones outside of Yosemite Valley are not as popular:
http://www.nps.gov/yose/planyourvisit/campground.htm
Tamarack Flat is a good choice because it's hard to get to. You drive several miles in on a dirt road. You don't need 4WD, but it's not paved.