I live in very central Berlin, and regularly go 'mountain' biking after work. You can ride from the city to endless forests in like 30 minutes in relative safety. There's also a huge amount of green space in the city itself.
I'm glad you put "mountain" in quotes, because we sure as hell don't have anything which counts as a mountain in this town - and no, that tiny hill in Humbolthain where the nazis built anti-air guns doesn't count.