"Long distance" is relative and I'd say exploring a giant city still fits within the description offered by @Darth_Biomech. I think the key aspect for what makes something an "adventure" is having each different location of the story have a distinct character and environment. If every scene can take place in the same sort of location, or a nondescript location, without affecting anything in the story, that's less of an adventure.
To take your "giant city" example: an adventure series would have the characters explore distinct parts of the city - the poor slums, the rich neighborhoods, the market district, the park, etc. A non-adventure story in the city might all take place in one area of the city or the same settings (only visiting seedy nightclubs that don't each have their own theme, for example). Or it could be a slice of life about someone who just lives in the city and regularly visits different parts of it - they live in a residential area, work downtown in a tower, go shopping at the market - but since these location changes are treated as mundane and usual, there's no "adventure" in that the character is experiencing something new when they go somewhere else.
An adventure also doesn't necessitate an especially large scale. If your main character is, say, a toddler or small child, you can definitely make an adventure story out of them exploring their neighborhood or a large house they've never been in. As long as the locations are new and different to the perspective character (and thus, the reader), that's an adventure in my eyes.