Another fun suggestion is the Afternoon Tea at the DLH. My girls have never wanted to do any character interactions, but my youngest loves Stitch. She asked to do Donald’s Seaside breakfast on her 10th birthday. It was very cute, the food was decent, and definitely a ton of character attention as our reservation was first thing in the morning. So much interaction with the characters that both of my girls said they were traumatized and never wanted to do another character meal.
Anyhow, the tea has no characters and has become a tradition/special treat for them.They have a kids menu option, and if it’s hot out (or just preferred), they will serve iced tea.
The princess breakfast at Napa Rose looks precious as well though but even more pricey than the tea.
ETA: They both also really enjoy Blue Bayou!
You have so many options! DLR is a really great place to celebrate birthdays.