I don't know if you're an ice cream connoisseur like me, but I love trying different ice creams and frozen custards and finding what is best anywhere I travel. Disney tends to disappoint me, since most of their ice cream parlors serve basic Edy's brand - the same stuff you can purchase in a grocery store. Boring. The Plaza Ice Cream Parlor, Beaches and Cream (seriously overrated), and even Ghirardelli fit that bill (although at Ghirardelli, the toppings and add-ons for sundaes make up for the basic ice cream). I'm assuming that you are looking for good ice cream that will satisfy everyone in your group, even whoever needs a non-dairy option.
The one ice cream place I have been seriously impressed by is Ample Hills Creamery at the Boardwalk. They make all of their ice cream, as well as brownies and butter cake for their sundaes, in house. They allowed me to sample a number of flavors, and I was impressed by all of them. I got a brownie sundae with the Ooey Gooey Butter Cake flavor. It was super rich and huge. My DH and I had to share - I would highly advise doing the same. The other flavor I really liked was the Oatmeal Lace. I haven't tried it, but they offer a non-dairy flavor called Lemon Sky. It doesn't sound like something I would typically choose, but I'm sure it would be more exciting than plain vanilla! Here's their menu:
https://disneyworld.disney.go.com/dining/boardwalk/ample-hills-creamery/menus/
One more idea. I haven't tried Vivoli il Gelato at Disney Springs (yet), but it looks like they have a number of "sorbettos," which I assume are probably dairy-free. Here's their menu:
https://disneyworld.disney.go.com/dining/disney-springs/vivoli-il-gelato/menus/
I hope that helps!