You don't mention the ages of your kids or your budget...
HDDR is our absolute favorite dining experience...no, make that overall experience, in all of WDW. It is a dinner show at Fort Wilderness that costs quite a bit of time and $$, but is well worth it, in our opinion. The food is not gourmet, but it's always been very good bbq ribs, fried chicken served in buckets, corn bread, salad, strawberry shortcake. The show is corny and silly, but we love it every time.
You might want to do one or 2 character meals, depending upon where you'll be or where you're staying, or which characters your kids like. We love to go to Chef Mickey's on our first night, it really gets us in the Disney mood. We have found that our experience is better in the main dining room as opposed to one of the side rooms, so if you go, politely ask to wait for a table in the main room. We've found more attention from the characters, plus you can watch the monorail gliding overhead. Another great character meal is Crystal Palace with Pooh and friends, and I've heard that 1900 Park Fair is fun and has great food, but I've never been.
Princess dining in the castle (CRT) is very special (you get to dine IN THE CASTLE!), and Akershus in Norway also has princesses in an interesting setting.
'Ohana is a fun restaurant in the Poly (you have to check out the Poly at night for its view of the lagoon, Electrical Water Pageant, and view of Wishes). The food is very good and they have fun games for kids.
Boma at AKL is very unique and California Grill has beautiful view of MK and Wishes.
I wouldn't call anything a "can't miss," you're in WDW, no family vacation is going to be a bust because you missed a good restaurant. We're trying all new places next time. Enjoy!