先週の日曜の場合、こんな感じでOK?
string viewDate = "";
DateTime dtNow = DateTime.Now;
DayOfWeek weekday = dtNow.DayOfWeek;
switch(weekday)
{
case DayOfWeek.Monday:
viewDate = dtNow.AddDays(-1).ToString("yyyy/MM/dd");
break;
case DayOfWeek.Tuesday:
viewDate = dtNow.AddDays(-2).ToString("yyyy/MM/dd");
break;
case DayOfWeek.Wednesday:
viewDate = dtNow.AddDays(-3).ToString("yyyy/MM/dd");
break;
case DayOfWeek.Thursday:
viewDate = dtNow.AddDays(-4).ToString("yyyy/MM/dd");
break;
case DayOfWeek.Friday:
viewDate = dtNow.AddDays(-5).ToString("yyyy/MM/dd");
break;
case DayOfWeek.Saturday:
viewDate = dtNow.AddDays(-6).ToString("yyyy/MM/dd");
break;
}
[追記]
日曜の場合は自分で考えてください。