The good news on in-park dining with finicky kids is almost every place will have kids' food no matter what. Every place will have chicken tenders, or hamburgers, or mac and cheese, or pizza.
MK: big fan of the breakfast at Crystal Palace. It's a buffet so there will be something for everybody, little cheaper than lunch/dinner, fun characters.
Be Our Guest is OK food, really fun atmosphere. I like the darker room to the left.
IMO the underrated eating spot at MK is Plaza Inn. It's a small house, no characters, no real theme. But because of the small size, the food is fresh and consistent. Good sandwiches and burgers, outstanding shakes and desserts. If you have a few introverts in your group, this would be a great place for those folks to recharge.
OH #### I forgot about eating inside Cinderella's Castle. It's a screwjob on the Dining Plan so you might want to consider paying out-of-pocket for it. But if meeting the Princesses is important to the girls and women in your life, this is the place to do it.
For something a little quicker... Cosmic Ray's in Tomorrowland. Burgers, tenders, sandwiches. The ordering stations look like they offer different things, but you canget the full menu at any register.
Pecos Bill recently redid a lot of their menu. Haven't been there since the change. I'll let another WDW expert with close personal ties to Pecos Bill speak on that place.
AK: Tusker House breakfast buffet is great, get to meet classic characters, and Jungle Juice for all within the sound of my voice.
Flametree BBQ place recently reopened after redoing the seating area. I'm not a fan, but I live in eastern Kansas with regular access to some of the best BBQ in the country. So I'm spoiled on BBQ.
Yak & Yeti sitdown IMO has dropped in quality over time, but the quick service counter is still pretty good. Operated by Landry's, so not technically a Disney restaurant.
Over on the AK side of the WDW grounds, my hidden gem is Sana'a at Animal Kingdom Lodge. Nice spot for a late lunch with a view of the big animals roaming the courtyards of AKL. The Na'an Bread Service is my favorite appetizer in the entire resort. Also a big fan of the Peri Peri Chicken. Good smoothies, too.
DHS: The only potential Star Wars dining will be if the Star Wars Launch Bay has expanded to add food and drink by May. Not sure what the timetable is on that.
For a family, my recommendation is the Sci-Fi Drive-In. The atmosphere is like an old drive-in, with the tables inside the bodies of old convertibles and dim lights on the ceiling simulating a starry night. Usually the screen runs old Sci-Fi movie trailers and clips, but they might be mixing in some Star Wars with that now.
One of the best snack places in any of the parks is Starring Rolls Cafe.
I'm had really good meals at Brown Derby, but I don't think it's a good value on the Dining Plan, and the pace might be a bit slow for the little kids.
Epcot: well, there's a lot of outstanding food in the World Showcase. Oh man. On the quick service level, I like all the teriyaki dishes at the Japan QSR. The casual Mexico place is really good. Via Napoli has waiter service but is a little more informal than the high-end stuff at Epcot. The pizzas are dynamite and the chicken parm is good and generously portioned. Akershus in Germany has a princess breakfast of ordinary food but a steady stream of Princesses greeting you at your table. I like Teppan Edo in Japan - it's one of those Japanese places where you sit at the grill and the chef cooks up the meats, veggies, rice, etc. right in front of you. I don't know if the show is any better than the best Japanese place in your home city, but the last time I ate there on the dining plan filet mignon was included as a regular credit.
If grandparents are coming and will take the kids one evening so the adults have a night out... Le Cellier in Canada. Outstanding steaks and breads. Don't overthink it. Get the filet.
My favorite dessert spot in Epcot is L'Artisan des Glaces in France. The macarons are phenomenal, all the ice creams there will be delicious, and they have a specialty dessert where they scoop ice cream into a warm Brioche mini-loaf and press it all together.
AVOID: Coral Reef. Looks like fun with the giant aquarium. But the food is a big disappointment especially with what else is available at Epcot.
UNDERRATED: Garden Grille. Rotating indoor restaurant, all you can eat, wait staff just keeps bringing stuff to the table, characters come to table to greet you in overalls and other farmer garb.
The Resorts are a big part of what makes the dining scene at WDW so vibrant and a destination for foodies. My favorite meal in all of WDW is dinner at Ohana at the Polynesian Resort. All you can eat, brought to your table, bread, salad, noodles, wings, potstickers, sirloin, chicken thighs, SHRIMP, with a couple of very special dipping sauces. There's also bread pudding, but I've never had it. My wife and daughter say it's really good. Most nights there's a really talented woman hosting the evening making announcements and directing traffic, also providing house music with ukulele melodies, operating a coconut-rolling race each hour for the kids, and passing out leis and inviting folks to dance. If MK has their fireworks show while you're there, the house will pipe in the music from the show and you will be able to see the fireworks from the restaurant.
I usually like it a little more laid-back, so I dig Whispering Canyon at Wilderness Lodge. If you eat there, no matter what you order, ask for ketchup at some point during the meal. Just trust me.
Best resort snack: beignets at Port Orleans French Quarter. We like to grab a half-dozen beignets, then take the boat from French Quarter to Disney Springs.
If there's a game you need to catch... ESPN Zone at Boardwalk. The on-site hotels will have local TV and all the Disney-owned cable channels including the ESPNs, but they won't have the FOX or Turner sports stations.
The Grand Floridian is a little too stuffy for me, but it is a beautiful resort. I'll let someone else review the restaurants there.
Disney Springs (formerly Downtown Disney) has undergone a major rebranding and rebuilding since I was there last. IIRC there are some outstanding Dining Plan deals to be had there, like Wolfgang Puck Express only counting as a QSR credit. My info on that is a bit dated, and they have opened a bunch of new places in the last year.