Hm. From Awakening, two stages come to mind for me:
The Great Mila Tree would be an absolutely gorgeous place to fight. Could have a 100% neutral layout on its branches without the need for gimmicks. Not much to say on the matter, but this would be a great place for Naga/Nagi/Tiki's theme to be remixed.
The Midmire from Ch10. Fighters would stand on one of the plateaus. Wyvern Riders coloured red and blue would occasionally descend to do battle with each-other; players can stand on their backs. The chapter this is from was an elevation for drama and emotion in Awakening, and featured one of the most magnificent tracks I have ever heard from the series. Even though it is really brown, I still think HD graphics can do it justice.
Stages from other games?
Well, nothing specific, but FE2 has some nice ideas. Like a shrine:
I apologize for the small graphic, but you get the idea. Not sure what they could do as far as gimmicks. Maybe the statues can release a flood of water that forces players to one side of the stage... like Norfair's lava, but instead of damage and launch, just push-back.
Also the game has a number of cemeteries with psychedelic zombies coming out of the ground. That would be awesome. It can be dark and moody but still have funky 8-bit-esque colour. Gaiden has amazing music so I'll take any excuse I can get to have some more in the game.
FE8 had that one chapter during Ephraim's route where you were on boat and attacked by monsters. That has a lot of possibility.
From the Tellius saga, I would want the run down, victorian-esque Streets of Daein. I just like the idea of a street fight being a thing in Smash Bros, and the art direction they took for each region in this game is magnificent.
They can always make it more Awakening-like by putting fortresses on the stage that instantly spawn warriors that OHKO within seconds of appearing.