Veletrzni Palac, Museum of Modern and Contemporary Art would be good for a 16 year old - it takes some finding, but the tram stops nearby - it’s over the river and off the beaten track for tourists. It has galleries devoted to 20th century Czech artists and explains limits on art in the communist era, as well as showing work by artists who died in concentration camps. I would start at the top on the 4th floor and work down. Good lively café next door - there’s a college in the other end of the building so lots of younger people around.
There’s a very big park between there and the river, with cafés etc. Good for a wander and people watching. Lots of students and families hanging out.
The building itself is interesting too - it was a purpose-built exhibition centre - called the Trade Palace.
The Municipal House was fantastic. You have to do a guided tour. Built entirely by Czech craftsman and designers, it was an important symbol of Czech independence. The art and architecture is incredible. Another good cafe (with robots collecting the dirty dishes when we were there!)
Finally, for art lovers, the Museum of Contemporary Glass was amazing. It’s not huge and very central.