In this anime I saw (it's been years), it seemed like a nice floating city, but something was going on (sadly, I 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 for by an old man. It turns out people who live down there need to be careful because the city sends out drones to check on them, and they are also searching for the boy. I think the girl had some weird powers, but I'm 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 didn't seem 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.)
I've ruled out:
- Battle Angel Alita
- Daphne in the Brilliant Blue
- Expelled From Paradise
- Astro Boy
- Kaiba