A bit of everyday
Why locals love it
I dare you not to have a good time here. So yeah, sure, it's mostly for kids, it's expensive as all hell and the attractions aren't all that. But very few places do you an amusement park smack in the middle of town. That alone merits at least an entry ticket. And It has one of the worlds oldest roller coasters.
Why you should visit it
For children in Copenhagen, a trip to Tivoli is something like a must or tradition. As mentioned, it's fairly expensive, but a great places for kids and the childish at the same time. It's also one of the two oldest parks of it's kind in the world. The other one if a bit outside the city.
During the summer, there's usually a Friday rock concert - mostly local acts, but also the odd international band.