French Quarter or Riverside are so right for a mother/daughter trip. Consider POR also. It's beautiful - all common areas are attractive, clean, & have a great welcoming "feel" to them.
A lot of good choices, you can't make a wrong decision, and you will have a great time no matter what you choose!
We found a good compromise that fits well for us... kinda what you're considering.... in that we get annual passes, always stay at BC (and try like heck to get the AP discount) and plan two trips in before the AP expires. Part of it is because we come from CA so we spread out coming to DW every 3, 4, 5 years. On the other hand, we like like the fact that when we do go, we know we'll be going twice within 12 months.
So I did vote BC, and wish you good luck. I know it can become complicated, but have a great trip!!