How many times have you read Goodnight Moon? In a day? In a week? In a row? If there is a young child in your life I bet there is A book that has been read until you can let your mind drift as you say the words from memory.
Kids love routines. They find comfort in them and a secure sense that they know what to expect and what is expected by them. Caregivers use this to help get through difficult transitions (like going to bed) and help ease anxieties.
So, why not leverage that with your museum visits as well? There is nothing wrong with visiting the same museum, or exhibit, or object multiple times. Kids will get comfortable with the space, you can look at the object from new angles and see new things and make new connections. You can slowly stretch the comfort level by connecting that object with something nearby, or something from a book or your home/classroom. When you do go somewhere new you can draw parallels to the favored spot and help bridge the gap.
If you are able to build a relationship with one museum you can connect with the education teams and visitor services (everyone you see out on the floor talking to visitors). You can take advantage of the resources they have, special programs going on or just the familiarity of really learning about something in a deep and meaningful way.
There is comfort in routines and that isn’t a bad thing. It is just up to you to figure out how to use it in a positive way.