Van likes bigger arenas with a wide range of different terrains within them (Old Mineshaft, Bastion Cliff, and especially Final Destination CAMPFC Edition). He also likes crazy and chaotic terrains (like ROTTA and RST Arena). He dislikes arenas with innocent bystanders and ones that don't offer him freedom of movement, especially floating platforms. His home terrain is the UPSS Perspicacity.
Solai likes simpler arenas, but ones with walls or structures for her to drive opponents against. Floating platforms work well too, especially if the opponent can't fly. She dislikes any terrain with neutral parties. Her home terrain is the Wilder Woods.
An antithesis consciousness doesn't really "like" or "dislike" anything, but because an antithesis consciousness is created to counter one person, it has a disadvantage anywhere the terrain can used to the other fighter's benefit. So in that sense it "favors" the simplest terrains out there. Its home terrain is the Big White.
Terrain-focused terrains are allowed for all three characters because it's more fun that way.
With that said:
Finalize Solai and Van I guess.
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"The courtroom is the garden of holy judgment. Those with lechery in their hearts should leave this sanctuary at once!" ~Franziska von Karma