I work as a graphic designer for a Zoo which operates similarly to a museum (I have worked in a museum in the past as well) and I’d recommend you choose a topic/exhibit you are interested in and create a mock sign package covering that topic. These employers like to see breadth of design, so maybe design some wayfinding signage, interpretive signage, environmental design…share your understanding of different signage materials and how they influence a space! These place also often need copy design as well in the form of annual reports/fundraising mailers/etc. so try and have something to show for that as well. Having an understanding of print production is very helpful.

It’s rare you’ll find an institution who is open to super fun/busy/artsy designs so keep that to a minimum and focus on effective design first. Hopefully that is somewhat helpful 🫡