The usual go-to solution is Google Calendar, but after having used it for a few months I believe its UI/UX doesn't fit this purpose and is hurting engagement.

I've googled and tried a few solutions, but none of them would let me easily create something like what you would see in an event website like skiddle.com or visitberlin.de.

Is everyone really re-inventing the wheel each time? I find it hard to believe.