I just found out this is a holiday in Slovenia and things may be closed. Anybody familiar with Ljubljana?
I can't find anything on the castle website to indicate that it ever closes. It seems unlikely that it's open 365 days a year, but who knows?
The National Museum doesn't include April 27 among its closing dates.
The Ethnographic Museum is closed on Mondays and holidays, per its website. Monday is a common closing day for museums, and April 27 is a Monday. The National Gallery will be closed because it's a Monday, but there's no indication it regularly closes on April 27, so persistent Googling may turn up other museums not regularly closed on Mondays that will be open on April 27.
Ljubljana is an architecturally lovely place, so your time will not be wasted if you just take to the streets.
You could also make a side-trip to Lake Bled by either bus or taxi. There's a train station around there somewhere, but I don't know how close it is to the lake.