Hi Christy!
Wow, that is so awesome that you are taking your teenage girls to Walt Disney World! I'm a guy and I actually really like Cinderella's Royal Table! Yes, there will be families that have little ones at Cinderella's Royal Table during dinner but it typically is not overwhelming. I have another awesome Magic Kingdom Table Service Dinning recommendation for you that I'm sure that your teenage girls will absolute love and it is the
Be Our Guest Restaurant in New Fantasyland. The Be Our Guest Restaurant is like stepping into the Beauty and the Beast Movie. Currently during dinner, which is a Table Service at the Be Our Guest Restaurant, the Ballroom, the Rose Gallery, and the West Wing rooms are open. Also during dinner at the Be Our Guest Restaurant, the Beast comes out to welcome his guests and then is available for photos in the Study. I would recommend that you make your Be Our Guest Restaurant Advanced Dining Reservations as soon as possible because the Be Our Guest Restaurant is extremely popular and it can be difficult to find openings for dinner.
Also I would encourage you to look at eating dinner at one of the Magic Kingdom Resorts because they are a short Monorail ride away from the Magic Kingdom. Here are some of my favorites:
At the Contemporary Resort-The California Grill or the Wave
At the Polynesian Resort-'Ohana or Kona Cafe
At the Grand Floridian Resort and Spa-Narcoossee's, Citricos, or the Grand Floridian Cafe
I hope that your next Walt Disney World vacation is truly magical in every way!
Keep Dreaming Big!
Marc