This is Petřín Lookout Tower (Petřínská rozhledna), a smaller cousin of Paris’ Eiffel tower, built only two years later. There’s a restaurant at the base and a long spiral stairway along the spine. It does not look like it, but the spine even contains an elevator.
I could have managed the stairway up, but I was curious and took the elevator instead. I was lucky, but you might have to wait in a row. Down I took the stairs and I suggest you do so as well, at least in one direction.