Is LEGO Batman: Legacy of the Dark Knight open-world?
Yes — Gotham is a free-roam open world with districts you unlock as the story progresses, in the spirit of LEGO Batman 2 and 3.
Gotham is a connected open world. Districts including Tricorner, Old Gotham South/North/West, The Cauldron, Newtown, Gotham Village, Robinson Park, East End and Amusement Mile unlock as you progress. The open world holds the bulk of the 200 WayneTech Caches plus AR Trials, Wanted Posters, Escaped Zoo Animals, Bat Symbols, Falcone Fortunes and Waylon Jones Cases. Many puzzles need characters unlocked later (Catwoman, Batgirl, Nightwing, Talia), so expect to revisit districts.