More information on the kids would help for sure. My kids (boys, 12 and 9) have enjoyed Garden Grill, Tusker House, and Chef Mickeys for character meals. They also love Sci Fi, T-Rex, Biergarten, Raglan Road, and BOG for non-character meals.
Welcome to the Dis. If your children are younger and girls, perhaps Akershus Royal Banquet Hall in the Norway Pavilion would be an interest. We went there for our first Disney trip when my daughter was 10 and she loved it; So much so she wanted to do it again when she was 14. It's also an ADR you can land with a last minute trip like you are planning.
Many of the popular dining choices can be very difficult to get into last minute. Places Like Chef Mickey ( food wise my least favorite) and Cinderella's Royal Table can be very difficult to get into under 180 days, but never give up. My advice is to go online and look at the different character dining experiences, choose the ones you want based off of the characters that appeal to you and then as soon as you have a vacation booked get online and start making your ADR's ASAP and be flexible with times. Late breakfast, early or late lunch and early dinners are much easier to secure.
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