Despite violence in the area, there seems to be a guarded ___ among inhabitants.

optimism（樂觀）與 guarded 形成固定搭配 a guarded optimism「審慎樂觀」，呼應 Despite violence 的轉折：雖有暴力，居民仍抱持謹慎的樂觀。語意完全吻合。