In one sense Tivoli isn't much different from a standard amusement park here in the states. It's filled with locals having fun.
Of course, seeing locals having fun in the USA isn't that interesting if you live in the USA. But it's a good way to get a glimpse at an aspect of Danish life when you're in Copenhagen.
To me, Tivoli didn't really resemble many US amusement parks I've been to. For one thing, it's right smack in the heart of the city. It is more like a park with amusements than an amusement park. I didn't notice the commercialism and product tie-ins you're likely to see in the US. It's a lovely place to walk around. I went there on my first evening in Copenhagen, after my long flight from the west coast, and I was jet lagged and it was a perfect way to relax and stay awake and try to adjust to the time change. I didn't go on any rides, just wandered about. It's hard to imagine visiting an amusement park in the US and not going on rides and still enjoying yourself.
I'm sure you can easily find some photos. If you want to see mine, they're in this album.
Have fun! Copenhagen is one of my favorite European cities.