I think we have similar needs/desires, lol! DH & I are childless, often travel with others who are childless, but love WDW and want atmosphere & good food!!!!
With that in mind, our favs/must-dos are:
Biergarten for sure!!! Amazing food, drink, service and atmosphere (oi, oi, oi!!!)
Bistro de Paris. This one's a bit more quiet and foodie, but the atmosphere, food and service is some of the best of WDW property. They also take the DDE. No children's menu and they don't accept the
DDP. Menu is really creative and the dining room is generally quiet
Jiko. Amazing wine list. Amazing. Generally very good service and excellent menu items. The filet over mac & cheese with the wine reduction was featured a year or so ago on the Food Channel. I would, however, urge you to just keep an eye on the reviews. The head chef just changed over, and I must say our portions were micro-sized since the change compared to years' worth of other visits. I'm hoping it was just an off night. Beautiful atmosphere. Go a bit early and check out the resort. Talk about atmosphere! There's a very nice lounge above another restaurant Boma. There's also a wine bar in the waiting room of Jiko.
Ohana, at least for breakfast. We've never gone for dinner and have seen hit or miss reviews, but the Mickey and Stitch character breakfast is too much fun, even for adults. The food is served family style, too, so no getting up to go to a buffet and possibly missing the characters at your table. Also, you don't have 200 people touching your serving utensils

It's a great way to start out your MK day -- seriously gets you in the spirit, especially if you're seated in the dining room that overlooks the castle. The place breaks out into song and dance with one of the popular songs from the movie Lilo & Stitch. Food is standard breakfast fare, eggs, bacon, sausage, a breakfast bread with pineapple in it, Mickey waffles.
Another vote for '50s PTC. Really unique atmosphere. Remember to keep your elbows on the table, wear a hat, don't take note of what color the soap is in the bathroom, and above all else, do not clean your plate
Those are our must-do TS choices. We've eaten at other places that honestly just don't wow us in the atmosphere nor food departments.
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CS -- really anywhere in Epcot in the World Showcase. The only place I personally wouldn't eat is America, lol, because I can get that any ole time. The CS is very, very good and very fun in Epcot.
MGM, avoid CS. Fill yourselves up at '50s PTC.
MK, our favorite CS is Pinocchio's Village Haus. If you get there early, you can get a seat that overlooks It's a Small World. Also, it's a nice change from burgers and pizza. Something has happened to the CS burgers in the last four months! Blech!!!!! Anyway, the Figero Fries at Pinocchio's Village Haus are something not to be missed. Think a BLT over a tub of french fries, with nacho cheese and ranch dressing on top. Good things
Columbia Harbor House at MK is also good, but the atmosphere is lacking a bit. It's just like any ole CS.
A hot dog at Casey's right there on Main Street, grab a table or shady patch of grass and enjoy the castle is pretty cool atmosphere. They're pretty good hot dogs, too.
Can't help on TS at AK. We haven't tried Yak n' Yetti, nor the new Tusker House. We do spend quite a bit of time at the Dwarma Bar in Africa, tho. They make a stellar -- STELLAR -- Bloody Mary. They don't accept the DDE, but if you tell them you have it, they'll make your drinks c-r-a-z-y strong. Asking for enough olives in the bloody marys' constitute a light lunch for us and we're good 'till dinnertime
I guess that's about it.
Have fun & welcome to the DIS!!!!!!!!