Oh my gosh there are soooo many to choose from! Here are some of my non character awesomely themed restaurants!
Sci Fi Dine In Theatre - In Hollywood Studios - the tables are set like cars and the whole theme is like a drive in movie that plays these old black and white monster movie type things. My kids LOVED this place!
50s Prime Time Cafe - Also in Hollywood Studios - Its themed around the 50s, so table manners are a thing, lol (no elbows on the tables and you must finish your plate before your desert!) I thought it was pretty funny, my older DS didn't think their should be "rules" when dining out at Disney, LOL
Whispering Canyon Cafe - In Wilderness Lodge - Can get very LOUD and has a ton of fun games that are played, lol...they only have like a couple bottles of ketchup so everytime you want ketchup the kids run around the place collecting ketchup and stuff, it was a ton of fun, we went there on our anniversary and they made my hubby sing to me, it was soooo funny. They do have coasters that you put on your table that says you want to play along or no you don't want to play along, but again it can get really LOUD.
TREX/Rainforest Cafe - Both places in Disney Springs w/ Rainforest also at Animal Kingdom. Food is generally the same, just whichever is your cup of tea...do your kids want to see Dinosaurs or Rainforest Animals (both places can get on the loud side too)
Teppen Edo - In Epcot - This is a disneyfied Hibachi place, I thought the food was pretty decent, but again it is disneyfied, so if you have been to a real hibachi grill you might be a little on the disappointed side. When we first ate there my oldest DS was disappointed, the next time we ate there my older DS actually requested it but again had no expectations, he basically was going because the food was pretty decent he though.
Biergarten - Also In Epcot - This is a fun place the theme is basically like a little town in germany and they have a band that comes out and plays as well. The only downside to this restaurant is, you are sat with other families, so it can be uncomfortable for some people. My older DS had a problem with this when we ate there, he didn't feel comfortable eating or talking in front of strangers. Me on the other hand could care less and striked up a conversation with everyone.
Coral Reef - Also In Epcot - Fun fish themed restaurant, it was fun watching all the fish as we were eating. Food was just ok though, nothing to rave about.