Plan on being in Prague at the end of May.
From your experience, what are 3 good day trips by train? Not interested in outdoor activities. Something like C. Krumlov charm (been there) would be great. Don’t think I would do more than one church and/or museum.
Konopiště, home of Archduke Franz Ferdinand
Rückl Crystal, in Nizbor. You can take a fascinating tour of the facility as they create the crystal products.
Plzeň - take a tour of Pilsner Urquell Brewery, but the city is also fascinating to walk around.
These can all be easily reached by train from Prague.
Plzen, as mentioned above, is a great one, and we recently visited Kutna Hora as a day trip from Prague. In addition to the famous bone church (Sedlec Ossuary) it's just a nice town to walk around, and it's less than an hour by train. You can also visit Karlstejn Castle as a day trip from Prague, tho I haven't personally done that one yet.
The spa town of Karlovy Vary is about 1-1/2 hours away by bus. The train takes a great deal longer. I haven't been to Karlovy Vary yet, but it sounds lovely and is on my list for a May visit this year.