How I did it: Well, I was lucky, really. Went to buy postcards in a museum and out in front I saw a banner stating that on our next national holiday the museum can be visited for free. So I checked at home if it was true for all museums. Luckily yes, so I could see 2 exhibitions I've wanted to for a long time.
Lessons & tips: Keep browsing event calendars and special tourists' sites that offer you a different experience from the usual/mainstream.