In this anime I saw (it's been years), it seemed like a nice floating city, but something was going on (sadly don't know the exact plot anymore), so the main character gets somehow chased by the police and falls off the city with this girl he met and as he wakes up from his fall he gets cared by an old man, and it turns out people who live down there need to be careful because the city sends out drones to check on them, also they are searching for the boy. I think the girl had some weird powers but not sure.
Also I recall them later being up on the floating city again but in the underground and he tries to get something done there, it's really futuristic down there (just dark and some guidelights which are stripes of light). But this part could also be from a different anime, it's been too long.
The boy should have given the girl to the police because of whatever she could do but refused, that's why both got chased. Maybe also because of something else but I think this was the main reason.
It's a series, not a game or anime movie. It seemed not like a new one, it could be about 5-10 years old or so. Also it's sadly not a really known one, I searched already in forums.
(Someone on MyAnimeList also seems to be searching for the exact same as far as I can tell)